Index of codesΒΆ
The codes
object may be used to access the codes that Sage can build.
BCHCode() |
A ‘Bose-Chaudhuri-Hockenghem code’ (or BCH code for short) is the largest possible cyclic code of length n over field F=GF(q), whose generator polynomial has zeros (which contain the set) ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
BinaryGolayCode() |
BinaryGolayCode() returns a binary Golay code. This is a perfect [23,12,7] code. It is also (equivalent to) a cyclic code, with generator polynomial ![]() |
CyclicCode() |
If g is a polynomial over GF(q) which divides ![]() ![]() ![]() |
CyclicCodeFromCheckPolynomial() |
If h is a polynomial over GF(q) which divides ![]() ![]() ![]() ![]() |
DuadicCodeEvenPair() |
Constructs the “even pair” of duadic codes associated to the “splitting” (see the docstring for is_a_splitting for the definition) S1, S2 of n. |
DuadicCodeOddPair() |
Constructs the “odd pair” of duadic codes associated to the “splitting” S1, S2 of n. |
ExtendedBinaryGolayCode() |
ExtendedBinaryGolayCode() returns the extended binary Golay code. This is a perfect [24,12,8] code. This code is self-dual. |
ExtendedQuadraticResidueCode() |
The extended quadratic residue code (or XQR code) is obtained from a QR code by adding a check bit to the last coordinate. (These codes have very remarkable properties such as large automorphism groups and duality properties - see [HP], Section 6.6.3-6.6.4.) |
ExtendedTernaryGolayCode() |
ExtendedTernaryGolayCode returns a ternary Golay code. This is a self-dual perfect [12,6,6] code. |
LinearCodeFromCheckMatrix() |
A linear [n,k]-code C is uniquely determined by its generator matrix G and check matrix H. We have the following short exact sequence |
QuadraticResidueCode() |
A quadratic residue code (or QR code) is a cyclic code whose generator polynomial is the product of the polynomials ![]() ![]() ![]() ![]() ![]() |
QuadraticResidueCodeEvenPair() |
Quadratic residue codes of a given odd prime length and base ring either don’t exist at all or occur as 4-tuples - a pair of “odd-like” codes and a pair of “even-like” codes. If ![]() ![]() ![]() |
QuadraticResidueCodeOddPair() |
Quadratic residue codes of a given odd prime length and base ring either don’t exist at all or occur as 4-tuples - a pair of “odd-like” codes and a pair of “even-like” codes. If n 2 is prime then (Theorem 6.6.2 in [HP]) a QR code exists over GF(q) iff q is a quadratic residue mod n. |
QuasiQuadraticResidueCode() |
A (binary) quasi-quadratic residue code (or QQR code), as defined by Proposition 2.2 in [BM], has a generator matrix in the block form ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
RandomLinearCode() |
The method used is to first construct a ![]() |
RandomLinearCodeGuava() |
The method used is to first construct a ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
ReedMullerCode() |
Returns a Reed-Muller code. |
ReedSolomonCode() |
NO DOCSTRING |
TernaryGolayCode() |
TernaryGolayCode returns a ternary Golay code. This is a perfect [11,6,5] code. It is also equivalent to a cyclic code, with generator polynomial ![]() |
ToricCode() |
Let ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
TrivialCode() |
NO DOCSTRING |
WalshCode() |
Returns the binary Walsh code of length ![]() ![]() |
Note
To import these names into the global namespace, use:
sage: from sage.coding.codes_catalog import *