Coding Theory

Partitioning of a Vector Space into Orbits by the Action of Automorphism Groups of Some Codes

Yu. L. Sagalovich


Abstract: Exact and asymptotic formulas are obtained for counting the number of orbits into which the space of $q^n$ vectors of length $n$ over the field $GF(q)$ is partitioned by the action of the minimal automorphism group of an arbitrary cyclic code and the automorphism group of the extended BCH code – an affine group. The calculations are carried out for $q=2$, $n=7,15,31$ and 8, 16, 32.

UDC: 621.391.15

Received: 29.01.1991

 English version: Problems of Information Transmission, 1992, 28:2, 147–153

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