Multisequence Shift Register Synthesis Over Commutative Rings With Identity With Applications to Decoding Cyclic Codes Over Integer Residue Rings
M.A. Armand · IEEE Transactions on Information Theory · 2004
We present a new algorithm for solving the multisequence shift register synthesis problem over a commutative ring R with identity. Given a finite set of R-sequences, each of length L, the complexity of our algorithm in terms of R-multiplications is O(L/sup 2/) as L /spl rarr/ /spl infin/. An important application of this algorithm is in the decoding of cyclic codes over Z/sub q/ up to the Hartmann-Tzeng bound, where q is a prime power. Characterization of the set of monic characteristic polynomials of a prescribed set of multiple syndrome sequences leads to an efficient decoding procedure, which we further extend to decode cyclic codes over Z/sub m/ where m is a product of prime powers.