Steklov Institute of Mathematics at St.Petersburg

PREPRINT 02/2007

ON LINEAR CODES WITH LARGE WEIGHTS SIMULTANEOULY FOR THE ROSENBLOOM--TSFASMAN AND HAMMING METRICS

This preprint was accepted January 22, 2007

ABSTRACT:
We show that maximum distance separable codes, or more
generally nearly maximum distance separable 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.