Z_p^k环上的BCH码的构造

Construction of BCH code over Z_p^k

BCH码是迄今为止所发现的一类性能优良的线性纠错码类,它具有很强的纠错能力。特别是它具有严格的代数结构,因此它在编码理论和实际中起着重要的作用。已知有限域Fp上长度为n=pm-1,设计距离为d的本原BCH码,在Galois环上通过对BCH码的生成多项式的Hensel提升,构造得到了Zpk环上的BCH码,且其最小距离至少为d。

BCH codes are of great practical importance for error correction. It has good structure of algebra. For a BCH code of length n =p^m - 1 and design distance over Fp , we lift its generator polynomial, and construct a BCH code over Zp^k . Moreover, the distance of new BCH code is at least d.