The structure of linear codes of constant weight

Author:
Jay A. Wood

Journal:
Trans. Amer. Math. Soc. **354** (2002), 1007-1026

MSC (2000):
Primary 94B05

DOI:
https://doi.org/10.1090/S0002-9947-01-02905-1

Published electronically:
October 26, 2001

MathSciNet review:
1867370

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Abstract: In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.

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Additional Information

**Jay A. Wood**

Affiliation:
Department of Mathematics, Computer Science & Statistics, Purdue University Calumet, Hammond, Indiana 46323, Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, and GRIM, Université Toulon-Var, 83957 La Garde Cedex, France

Address at time of publication:
Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, Michigan 49008–5248

Email:
jay.wood@wmich.edu

DOI:
https://doi.org/10.1090/S0002-9947-01-02905-1

Keywords:
Constant weight codes,
Lee weight,
Euclidean weight,
extension theorem,
orbital codes,
virtual codes

Received by editor(s):
January 15, 2001

Published electronically:
October 26, 2001

Additional Notes:
Partially supported by Purdue University Calumet Scholarly Research Awards. Some results were announced in [17] and [18]. Theorem 10.3 first appeared in [15]

Article copyright:
© Copyright 2001
American Mathematical Society