Title :
A transform theory for a class of group-invariant codes
Author :
Tanner, R. Michael
Author_Institution :
Dept. of Comput. & Inf. Sci., California Univ., Santa Cruz, CA, USA
fDate :
7/1/1988 12:00:00 AM
Abstract :
A binary cyclic code of length of n can be defined by a set of parity-check equations that is invariant under the additive cyclic group generated by A:i→i+1 modulo n. A class of quasicyclic codes that have parity-check equations invariant under the group generated by a subgroup of A and a subgroup of the multiplicative group M:i →2ki modulo n is studied in detail. The Fourier transform transforms the action of the additive group, and a linearized polynomial transform transforms the action of the multiplicative group. The form of the transformed code equations permits a BCH-like bound on the minimum distance of the code. The techniques are illustrated by the construction of several codes that are decodable by the Berlekamp-Massey algorithm and that have parameters that approach or surpass those of the best codes known
Keywords :
error correction codes; transforms; BCH-like bound; Berlekamp-Massey algorithm; Fourier transform; additive group; binary cyclic code; group-invariant codes; linearized polynomial transform; minimum distance; multiplicative group; parity-check equations; quasicyclic codes; transform theory; Decoding; Electronic circuits; Equations; Error correction codes; Feedback; Fourier transforms; Information theory; Parity check codes; Polynomials; Shift registers;
Journal_Title :
Information Theory, IEEE Transactions on