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

Pages: 579 - 596, Volume 4, Issue 4, November 2010

doi:10.3934/amc.2010.4.579       Abstract        References        Full Text (298.6K)       Related Articles

Annika Meyer - Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, 52062 Aachen, Germany (email)

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.

Keywords:  Linear code, self-orthogonal code, weight distribution, extremality.
Mathematics Subject Classification:  11T71.

Received: February 2010;      Revised: September 2010;      Published: November 2010.

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