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https://doi.org/10.1109/TIT.2003.821966
Title: | Multisequence shift register synthesis over commutative rings with identity with applications to decoding cyclic codes over integer residue rings | Authors: | Armand, M.A. | Keywords: | Cyclic codes Decoding Galois rings Minimal polynomials Sequences |
Issue Date: | Jan-2004 | Citation: | 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 | URI: | http://scholarbank.nus.edu.sg/handle/10635/82736 | ISSN: | 00189448 | DOI: | 10.1109/TIT.2003.821966 |
Appears in Collections: | Staff Publications |
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