D.10.2 decodegb_lib

Library:

decodegb.lib

Purpose:

Decoding and min distance of linear codes with GB

Author:

Stanislav Bulygin, [email protected]

Overview:

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.

Procedures:

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