Transactions of the American Mathematical Society

Author(s): Jay A. Wood
Journal: Trans. Amer. Math. Soc. 354 (2002), 1007-1026.
MSC (2000): Primary 94B05
Posted: October 26, 2001
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Abstract: In this paper we determine completely the structure of linear codes over $\mathbb Z/N\mathbb Z$ 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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 94B05

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: 10.1090/S0002-9947-01-02905-1
PII: S 0002-9947(01)02905-1
Keywords: Constant weight codes, Lee weight, Euclidean weight, extension theorem, orbital codes, virtual codes
Received by editor(s): January 15, 2001
Posted: 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]
Copyright of article: Copyright 2001, American Mathematical Society

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