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Completely regular codes and completely transitive codes

✍ Scribed by Patrick Solé

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
511 KB
Volume
81
Category
Article
ISSN
0012-365X

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✦ Synopsis

A binary code C is said to be completely regular if the weight distribution of any translate x + C depends only on the distance of x to C.

Such codes are related to designs and distance regular graphs. Their covering radius is equal to their external distance. All perfect and uniformly packed codes are known to be completely regular.

We construct new examples of a different kind, including the nonlinear extended Preparata and Goethals codes. Three constructions are given: direct sum, extension, and action of the automorphism group of the code. We introduce the class of completely transitive codes which seems to be strictly contained in the class of completely regular codes. A sufficient condition for complete transitivity is given.

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