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article · IEEE Transactions on Information Theory · 2004

Multisequence Shift Register Synthesis Over Commutative Rings With Identity With Applications to Decoding Cyclic Codes Over Integer Residue Rings

M.A. Armand

Cited by 9Abstract and details only

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(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.

Cite this paper

APA 7

Armand, M. (2004). 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. https://doi.org/10.1109/tit.2003.821966

MLA 9

Armand, M.A. “Multisequence Shift Register Synthesis Over Commutative Rings With Identity With Applications to Decoding Cyclic Codes Over Integer Residue Rings.” IEEE Transactions on Information Theory, vol. 50, no. 1, 2004, pp. 220–29, https://doi.org/10.1109/tit.2003.821966.

Chicago

Armand, M.A. 2004. “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): 220–29. https://doi.org/10.1109/tit.2003.821966.

Harvard

Armand, M. (2004) ‘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), pp. 220–229. Available at: https://doi.org/10.1109/tit.2003.821966.

BibTeX
@article{armand2004multisequence,
  title = {{Multisequence Shift Register Synthesis Over Commutative Rings With Identity With Applications to Decoding Cyclic Codes Over Integer Residue Rings}},
  author = {Armand, M.A.},
  journal = {IEEE Transactions on Information Theory},
  volume = {50},
  number = {1},
  pages = {220--229},
  year = {2004},
  doi = {10.1109/tit.2003.821966}
}

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