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m-adic residue codes

机译：m-adic残基代码

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摘要

The m-adic residue codes are investigated and are found to have many of the strong properties of the quadratic residue codes. A subgroup of the automorphism group and restrictions on the form of the idempotents of the m-adic residue codes are given. It is shown that some m-adic residue codes are self-orthogonal and the duals of some m-adic residue codes are their complements. Bounds on the minimum of the weights of the odd-like vectors in the odd-like codes are given. At some lengths, m-adic residue codes exist for several values of m. Containment relationships between these codes are demonstrated which show that, when m is even, m-adic residue codes inherit properties of quadratic residue codes. A table is included that contains minimum weights of the binary m-adic residue codes of lengths less than or equal to 127.
机译：研究了m-adic残基代码，发现它们具有二次残基代码的许多强大特性。给出了自同构群的一个亚群以及对m-adic残基编码的幂等形式的限制。结果表明，一些m-adic残基代码是自正交的，一些m-adic残基代码的对偶是它们的补码。给出了奇数码中奇数矢量的权重最小值的界。在某些长度下，存在多个m值的m-adic残基代码。这些代码之间的包含关系得到证明，表明当m为偶数时，m-adic残基代码继承了二次残基代码的性质。包含一个表，该表包含长度小于或等于127的二进制m-adic残基代码的最小权重。

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