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A transform theory for a class of group-invariant codes

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1 Author(s)
Tanner, R.M. ; Dept. of Comput. & Inf. Sci., California Univ., Santa Cruz, CA, USA

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:ii+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

Published in:

Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 4 )