Properties of dual codes defined by nondegenerate forms

Year 2017, Volume: 4 Issue: 2 (Special Issue: Noncommutative rings and their applications), 105 - 113, 10.01.2017

Steve Szabo Jay A. Wood

https://doi.org/10.13069/jacodesmath.284934

Cited By: 3

Abstract

Dual codes are defined with respect to non-degenerate sesquilinear or bilinear forms over a finite
Frobenius ring. These dual codes have the properties one expects from a dual code: they satisfy
a double-dual property, they have cardinality complementary to that of the primal code, and they
satisfy the MacWilliams identities for the Hamming weight.

Keywords

Frobenius ring, Sesquilinear form, Bilinear form, Dual code, Generating character, MacWilliams identities

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