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Error Control codes algorithms

There are realized four algorithms:

Berlekamp–Massey algorithm | Алгоритм Берлекэмпа-Мэсси для решения ключевого уравнения

BMA(S, t, eps_0, debug = False) # Standart BM algorithm
BMA2(S, t, debug = False) # The second realization of BM (the result should be equal)
BMARS(S, t, debug = False) # The BM algorithm to find Psi(x) - polynom of errors and erasure
  • S - the dictionary of syndromes started with the index of 1: {1: S1, 2: S2, ..., n: Sn}
  • t - the minimum amount of error the code can detect
  • eps_0 - the element of Galois field (see Galois Field realization) of power 0 - eps^0 gf(0)
  • debug - the flag to see full information about the algorithm proccess (in russian language)

Piterson-Gorenshtein-Zirler algorith | Алгоритм Питерсона-Горенштейна-Цирлера для решения ключевого уравнения

PGCA(S, t, degub = False)
  • S - the dictionary of syndromes started with the index of 1: {1: S1, 2: S2, ..., n: Sn}
  • t - the minimum amount of error the code can detect
  • debug - the flag to see full information about the algorithm proccess (in russian language)

Euclid algorith to solve key equation | Алгоритм Евклида для решения ключевого уравнения

EuA(S, t, debug = False)
EuA2(S, t, debug = False) # second realization
  • S - the dictionary of syndromes started with the index of 1: {1: S1, 2: S2, ..., n: Sn}
  • t - the minimum amount of error the code can detect
  • debug - the flag to see full information about the algorithm proccess (in russian language)

Chen algorith to find roots of error locator polynomial | Алгоритм Ченя для нахождения корней полинома локаторов ошибок

ChenA(Lambda, field, debug = False)
  • Lambda - error locator polynomial of type DPoly (see GF documentations)
  • field - Galois field (also see GF documentations)
  • debug - the flag to see full information about the algorithm proccess (in russian language)

Forni algorithm to find the values of mistakes | Алгоритм Форни для нахождения значений ошибок

ForniA(roots, Omega, Lambda, t, debug = False)
ForniA(roots, Omega, Lambda, t, b, debug = False) # the same as the first ForniA, but with parameter "b" as the parameter of RS code