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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The structure of linear codes of constant weight
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by Jay A. Wood
Trans. Amer. Math. Soc. 354 (2002), 1007-1026
DOI: https://doi.org/10.1090/S0002-9947-01-02905-1
Published electronically: 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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Bibliographic 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
  • MR Author ID: 204174
  • Email: jay.wood@wmich.edu
  • 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]
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 1007-1026
  • MSC (2000): Primary 94B05
  • DOI: https://doi.org/10.1090/S0002-9947-01-02905-1
  • MathSciNet review: 1867370