环Z_4上负循环码的代数译码
Algebraic Decoding of Negacyclic Codes Over Z_4
摘要：
在这篇文章中，我们调查Berlekamp的非循环码，并发现这些代码，当考虑在整数模4，不受任何限制的最小距离Berlekamp的原始文件中观察到的。这里考虑的码的最小Lee距离至少为2 t +1，其中码的生成多项式的根为z，z^3，.，z^{2 t +1}，对于Z4的伽罗瓦扩张中的本原2阶单位根z。对t没有限制。我们提出了这类码的代数译码算法，它能纠正李权码在t以内的任何错误模式。我们的处理使用Grobner基地和解码复杂度是平方的t。
英文摘要：
In this article we investigate Berlekamp's negacyclic codes and discover that these codes, when considered over the integers modulo 4, do not suffer any of the restrictions on the minimum distance observed in Berlekamp's original papers. The codes considered here have minimim Lee distance at least 2t+1, where the generator polynomial of the code has roots z,z^3,...,z^{2t+1} for a primitive 2nth root of unity z in a Galois extension of Z4. No restriction on t is imposed. We present an algebraic decoding algorithm for this class of codes that corrects any error pattern of Lee weight at most t. Our treatment uses Grobner bases and the decoding complexity is quadratic in t.
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