模循环码和p-adic循环码
Modular and p-adic cyclic codes
摘要：
本文给出了模p^a整数环上和p进数上长度为n的循环码的结构的一些基本定理，其中p是不整除n的素数。一个特别有趣的例子是长度为7的2-adic循环码，其生成多项式为X^3 + lambda X^2 +（lambda - 1）X - 1，其中lambda满足lambda X^2- lambda + 2 =0。这是二进制汉明码和四进制八进制码（后者相当于Nordstrom-Robinson码）的2-adic推广。其他示例包括长度为24的2-adic Golay码和长度为12的3-adic Golay码。
英文摘要：
This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo p^a and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomial X^3 + lambda X^2 + (lambda - 1) X - 1, where lambda satisfies lambda^2 - lambda + 2 =0. This is the 2-adic generalization of both the binary Hamming code and the quaternary octacode (the latter being equivalent to the Nordstrom-Robinson code). Other examples include the 2-adic Golay code of length 24 and the 3-adic Golay code of length 12.
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