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Multisequence shift register synthesis over commutative rings with identity with applications to decoding cyclic codes over integer residue rings

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1 Author(s)
Armand, M.A. ; Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore

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(L2) as L → ∞. An important application of this algorithm is in the decoding of cyclic codes over Zq 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 Zm where m is a product of prime powers.

Published in:

Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 1 )

Date of Publication:

Jan. 2004

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