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Transactions of the American Mathematical Society

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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
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 $\mathbb Z/N\mathbb Z$ 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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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

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