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D.10.2 decodegb_lib

Decoding and min distance of linear codes with GB
Stanislav Bulygin, bulygin@mathematik.uni-kl.de

In this library we generate several systems used for decoding cyclic codes and finding their minimum distance. Namely, we work with the Cooper's philosophy and generalized Newton identities. The origindeal method of quadratic equations is worked out here as well. We also (for comparison) enable to work with the system of Fitzgerald-Lax. We provide some auxiliary functions for further manipulations and decoding. For an overview of the methods mentioned above Decoding codes with Groebner bases. For the vanishing ideal computation the algorithm of Farr and Gao is implemented.


D.10.2.1 sysCRHT  generates the CRHT-ideal as in Cooper's philosophy
D.10.2.2 sysCRHTMindist  CRHT-ideal to find the minimum distance in the binary case
D.10.2.3 sysNewton  generates the ideal with the generalized Newton identities
D.10.2.4 sysBin  generates Bin system using Waring function
D.10.2.5 encode  encodes given message x with the given generator matrix g
D.10.2.6 syndrome  computes a syndrome w.r.t. the given check matrix
D.10.2.7 sysQE  generates the system of quadratic equations for decoding
D.10.2.8 errorInsert  inserts errors in a word
D.10.2.9 errorRand  inserts random errors in a word
D.10.2.10 randomCheck  generates a random check matrix
D.10.2.11 genMDSMat  generates an MDS (actually an RS) matrix
D.10.2.12 mindist  computes the minimum distance of a code
D.10.2.13 decode  decoding of a word using the system of quadratic equations
D.10.2.14 decodeRandom  a procedure for manipulation with random codes
D.10.2.15 decodeCode  a procedure for manipulation with the given code
D.10.2.16 vanishId  computes the vanishing ideal for the given set of points
D.10.2.17 sysFL  generates the Fitzgerald-Lax system
D.10.2.18 decodeRandomFL  manipulation with random codes via Fitzgerald-Lax