Vol. 2, No. 2, 2009

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On distances and self-dual codes over $F_q[u]/(u^t)$

Ricardo Alfaro, Stephen Bennett, Joshua Harvey and Celeste Thornburg

Vol. 2 (2009), No. 2, 177–194
Abstract

New metrics and distances for linear codes over the ring Fq[u](ut) are defined, which generalize the Gray map, Lee weight, and Bachoc weight; and new bounds on distances are given. Two characterizations of self-dual codes over Fq[u](ut) are determined in terms of linear codes over Fq. An algorithm to produce such self-dual codes is also established.

Keywords
linear codes over rings, self-dual codes
Mathematical Subject Classification 2000
Primary: 94B05, 94B60
Secondary: 11T71
Milestones
Received: 21 August 2008
Revised: 10 December 2008
Accepted: 13 January 2009
Published: 7 May 2009

Communicated by Nigel Boston
Authors
Ricardo Alfaro
Mathematics Department
University of Michigan–Flint
Flint, MI 48502
United States
Stephen Bennett
Mathematics Department
University of Michigan–Flint
Flint, MI 48502
United States
Joshua Harvey
Mathematics Department
University of Michigan–Flint
Flint, MI 48502
United States
Celeste Thornburg
Mathematics Department
University of Michigan–Flint
Flint, MI 48502
United States