On dual extremal maximal self-orthogonal codes of Type I-IV

Annika Meyer

doi:10.3934/amc.2010.4.579

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2010, Volume 4, Issue 4: 579-596. Doi: 10.3934/amc.2010.4.579

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On dual extremal maximal self-orthogonal codes of Type I-IV

Annika Meyer^1,

1.
Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, 52062 Aachen

Received: January 31, 2010

Revised: August 31, 2010

Published: October 2010

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Abstract

For a Type $T \in${I, II, III, IV} of codes over finite fields and length $N$ where there exists no self-dual Type $T$ code of length $N$, upper bounds on the minimum weight of the dual code of a self-orthogonal Type $T$ code of length $N$ are given, allowing the notion of dual extremal codes. It is proven that for $T \in${II, III, IV} the Hamming weight enumerator of a dual extremal maximal self-orthogonal Type $T$ code of a given length is unique.

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Mathematics Subject Classification: 11T71.

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