private static IEnumerable <FieldElement[]> PlaceErrors(GaloisField field,
int codewordLength,
IReadOnlyList <int> errorsPositions,
IList <int> noiseValue,
int currentErrorPosition)
{
if (currentErrorPosition == errorsPositions.Count)
{
var additiveNoise = Enumerable.Repeat(field.Zero(), codewordLength).ToArray();
for (var i = 0; i < errorsPositions.Count; i++)
{
additiveNoise[errorsPositions[i]] = field.CreateElement(noiseValue[i]);
}
yield return(additiveNoise);
yield break;
}
for (var i = noiseValue[currentErrorPosition]; i < field.Order; i++)
{
noiseValue[currentErrorPosition] = i;
foreach (var additiveNoise in PlaceErrors(field, codewordLength, errorsPositions, noiseValue, currentErrorPosition + 1))
{
yield return(additiveNoise);
}
}
noiseValue[currentErrorPosition] = 1;
}
internal StandardReedSolomonCode(
GaloisField field,
int codewordLength,
int informationWordLength,
IDecoder decoder,
IListDecoder listDecoder)
{
Field = field;
CodewordLength = codewordLength;
InformationWordLength = informationWordLength;
CodeDistance = CodewordLength - InformationWordLength + 1;
_decoder = decoder;
_listDecoder = listDecoder;
_preparedPoints = Enumerable.Range(0, CodewordLength)
.Select(x => Field.CreateElement(Field.GetGeneratingElementPower(x)))
.ToArray();
_maxListDecodingRadius = (int)Math.Ceiling(CodewordLength - Math.Sqrt(CodewordLength * (CodewordLength - CodeDistance)) - 1);
}
static BiVariablePolynomialTests()
{
Gf5 = new PrimeOrderField(5);
var polynomialForEvoluation = new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 1)] = Gf5.CreateElement(2),
[new Tuple <int, int>(0, 1)] = Gf5.One(),
[new Tuple <int, int>(2, 0)] = Gf5.One(),
[new Tuple <int, int>(1, 0)] = Gf5.One(),
[new Tuple <int, int>(0, 0)] = Gf5.CreateElement(4)
};
EvaluateTestsData
= new TheoryData <EvaluationTestCase>
{
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.One(),
YValue = Gf5.CreateElement(3),
Expected = Gf5.Zero()
},
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.CreateElement(2),
YValue = new FieldElement(Gf5, 4),
Expected = Gf5.Zero()
},
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.CreateElement(3),
YValue = Gf5.CreateElement(2),
Expected = Gf5.Zero()
},
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.CreateElement(2),
YValue = Gf5.CreateElement(3),
Expected = Gf5.Zero()
},
};
AddTestsData
= new TheoryData <BinaryOperationTestCase>
{
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 1)] = Gf5.CreateElement(4),
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(0, 0)] = Gf5.One()
}
}
};
SubtractTestsData
= new TheoryData <BinaryOperationTestCase>
{
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.One()
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4)
}
}
};
MultiplyPolynomialsTestsData
= new TheoryData <BinaryOperationTestCase>
{
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.CreateElement(2)
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(2, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 2)] = Gf5.CreateElement(3)
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5),
Expected = new BiVariablePolynomial(Gf5)
}
};
var polynomialForMultiplication
= new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4),
[Tuple.Create(1, 1)] = Gf5.One()
};
MultiplyByFieldElementTestsData
= new TheoryData <MultiplicationByFieldElementTestCase>
{
new MultiplicationByFieldElementTestCase
{
Polynomial = polynomialForMultiplication,
Multiplier = Gf5.Zero(),
Expected = new BiVariablePolynomial(Gf5)
},
new MultiplicationByFieldElementTestCase
{
Polynomial = polynomialForMultiplication,
Multiplier = Gf5.CreateElement(2),
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.CreateElement(2)
}
}
};
SubstitutionTestsData
= new TheoryData <SubstitutionTestCase>
{
new SubstitutionTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
XSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.One()
},
YSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.One()
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.CreateElement(2)
}
},
new SubstitutionTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.One()
},
XSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.One()
},
YSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 1)] = Gf5.One()
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.CreateElement(4),
[Tuple.Create(2, 1)] = Gf5.One()
}
},
new SubstitutionTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
XSubstitution = new BiVariablePolynomial(Gf5),
YSubstitution = new BiVariablePolynomial(Gf5),
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One()
}
}
};
DivideByXDegreeTestsData
= new TheoryData <DivideByXDegreeTestCase>
{
new DivideByXDegreeTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.CreateElement(3)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3)
}
},
new DivideByXDegreeTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3)
}
},
new DivideByXDegreeTestCase
{
Polynomial = new BiVariablePolynomial(Gf5),
Expected = new BiVariablePolynomial(Gf5)
}
};
EvaluateXTestsData
= new TheoryData <PartialEvaluationTestCase>
{
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.One()
},
VariableValue = Gf5.One(),
Expected = new Polynomial(Gf5, 0, 1)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 1)] = Gf5.One()
},
VariableValue = Gf5.Zero(),
Expected = new Polynomial(Gf5, 3)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(2, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.One(),
[Tuple.Create(0, 2)] = Gf5.One()
},
VariableValue = Gf5.CreateElement(3),
Expected = new Polynomial(Gf5, 4, 4, 1)
}
};
EvaluateYTestsData
= new TheoryData <PartialEvaluationTestCase>
{
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
VariableValue = Gf5.One(),
Expected = new Polynomial(Gf5, 0, 1)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(1, 1)] = Gf5.One()
},
VariableValue = Gf5.Zero(),
Expected = new Polynomial(Gf5, 3)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(2, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.One(),
[Tuple.Create(0, 2)] = Gf5.One()
},
VariableValue = Gf5.CreateElement(2),
Expected = new Polynomial(Gf5, 3, 0, 2)
}
};
HasseDerivativeCalculationTestsData
= new TheoryData <HasseDerivativeCalculationTestCase>
{
new HasseDerivativeCalculationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 2)] = Gf5.One()
},
R = 1,
S = 1,
XValue = Gf5.One(),
YValue = Gf5.One(),
Expected = Gf5.Zero()
},
new HasseDerivativeCalculationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(2, 2)] = Gf5.One()
},
R = 1,
S = 1,
XValue = Gf5.One(),
YValue = Gf5.One(),
Expected = new FieldElement(Gf5, 4)
},
new HasseDerivativeCalculationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(2, 2)] = Gf5.One()
},
R = 2,
S = 1,
XValue = Gf5.One(),
YValue = Gf5.One(),
Expected = Gf5.CreateElement(2)
}
};
}
