In this paper, we construct many infinite families of distance-optimal codes with new parameters, some of which are bchcodes and quasi-cyclic codes. In particular, we report the first infinite family of binary distan...
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In this paper, we construct many infinite families of distance-optimal codes with new parameters, some of which are bchcodes and quasi-cyclic codes. In particular, we report the first infinite family of binary distance-optimal bchcodes with the minimum distance 8. Secondly, several infinite families of binary bch codes and quasi-cyclic codes are presented. Many codes in these families have optimal or best known parameters. Thirdly, we construct infinite families of binary cyclic [n,>= n+1/2, d](2) codes with minimum distances d >= [n-1/Pi(s)(i =1) p(i)], n = (2(p1) - 1)(2(p2) - 1) center dot center dot center dot (2(ps) - 1), p(1),..., p(s) are different primes. Our construction extends the main result of a recent paper published by Sun et al. to much more general binary cyclic codes with various lengths. We also construct an infinite family of binary quasi-cyclic codes with the rate around 1 2 and relative minimum distance lower bounded by O( 1/log(2) log(2) n).
This paper presents a new syndrome calculation method to reduce hardware complexity for bch decoding. Compared to previous works that calculate all 2t syndromes simultaneously in the syndrome calculation (SC) stage, t...
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ISBN:
(纸本)9788995004449
This paper presents a new syndrome calculation method to reduce hardware complexity for bch decoding. Compared to previous works that calculate all 2t syndromes simultaneously in the syndrome calculation (SC) stage, the proposed architecture schedules the syndrome calculation to reduce the hardware complexity;odd-indexed syndromes are computed in the SC stage, while even-indexed syndromes are computed when they are needed in the key-equation solving (KES) stage. Experimental results show that the proposed architecture saves 65% of hardware resources compared to the conventional architecture.
A new bound on the distance of binary cyclic codes is proposed. The approach is based on the representation of a subset of the roots of the generator polynomial by a rational function. A new bound on the minimum dista...
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ISBN:
(纸本)9781457705953
A new bound on the distance of binary cyclic codes is proposed. The approach is based on the representation of a subset of the roots of the generator polynomial by a rational function. A new bound on the minimum distance is proven and several classes of binary cyclic codes are identified. For some classes of codes, this bound is better than the known bounds (e. g. bch or Hartmann-Tzeng bound). Furthermore, a quadratic-time decoding algorithm up to this new bound is developed.
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