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|Title:||Multisequence shift register synthesis over commutative rings with identity with applications to decoding cyclic codes over integer residue rings|
|Source:||Armand, M.A. (2004-01). Multisequence shift register synthesis over commutative rings with identity with applications to decoding cyclic codes over integer residue rings. IEEE Transactions on Information Theory 50 (1) : 220-229. ScholarBank@NUS Repository. https://doi.org/10.1109/TIT.2003.821966|
|Abstract:||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.|
|Source Title:||IEEE Transactions on Information Theory|
|Appears in Collections:||Staff Publications|
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