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Z8-Cyclic Codes and Quadratic Residue Codes

✍ Scribed by Mei Hui Chiu; Stephen S.-T Yau; Yung Yu

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 160 KB
Volume: 25
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2000.0687

No coin nor oath required. For personal study only.

✦ Synopsis

In memory of Professor Gian-Carlo Rota for his great contributions in combinatorial and discrete geometry A set of n-tuples over 8 is called a code over 8 or a 8 code if it is a 8 module. A particularly interesting family of 8 -cyclic codes are quadratic residue codes. We define such codes in terms of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field. In particular we show that the quadratic residuce codes over 8 have large automorphism groups which will be useful in decoding these codes by using the powerful permutation decoding methods described by F. J. MacWilliams and N. J. A. Sloane (1978, "Theory of Error-Correcting Codes," North-Holland, Amsterdam). We also define a distance preserving map from N 8 (Lee distance) to 4N 2 (Hamming distance).

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