Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 94B05

Retrieve articles in all journals with MSC (2000): 94B05


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: http://dx.doi.org/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
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