On linear codes with large weights simultaneously for the Rosenbloom--Tsfasman and Hamming metrics

Authors:
M. M. Skriganov
Affiliations:
Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
Venue:
Journal of Complexity
Year:
2007

Citing 3
Cited 0

Introduction to Coding Theory

Introduction to Coding Theory
The automorphism group of a linear space with the Rosenbloom—Tsfasman metric

European Journal of Combinatorics
Low-Discrepancy Sequences and Global Function Fields with Many Rational Places

Finite Fields and Their Applications

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Abstract

We show that maximum distance separable (MDS) codes, or more generally nearly MDS codes, for the Rosenbloom-Tsfasman metric can meet the Gilbert-Varshamov bound for their Hamming weights. The proof is based on a careful analysis of orbits of a linear group preserving the Rosenbloom-Tsfasman metric.