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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 679–702 (Mi mmj580)  

On linear ordered codes

Alexander Bargab, Woomyoung Parkcb

a Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow, Russia
b Dept. of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA
c Samsung Electronics, Suwon, Gyeonggi-do, Korea

Abstract: We consider linear codes in the metric space with the Niederreiter–Rosenbloom–Tsfasman (NRT) metric, calling them linear ordered codes. In the first part of the paper we examine a linear-algebraic perspective of linear ordered codes, focusing on the distribution of “shapes” of codevectors. We define a multivariate Tutte polynomial of the linear code and prove a duality relation for the Tutte polynomial of the code and its dual code. We further relate the Tutte polynomial to the distribution of support shapes of linear ordered codes, and find this distribution for ordered MDS codes. Using these results as a motivation, we consider ordered matroids defined for the NRT poset and establish basic properties of their Tutte polynomials. We also discuss connections of linear ordered codes with simple models of information transmission channels.

Key words and phrases: ordered metrics, linear codes, poset matroids, binomial moments, higher poset weights, wiretap channel.

Funding Agency Grant Number
National Science Foundation CCF1217894
CCF0916919
The first named author supported in part by NSF grants CCF1217894, CCF0916919. The second named author supported by NSF grant CCF0916919.


DOI: https://doi.org/10.17323/1609-4514-2015-15-4-679-702

Full text: http://www.mathjournals.org/.../2015-015-004-006.html
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Bibliographic databases:

MSC: 94B25
Received: February 18, 2015; in revised form July 23, 2015
Language:

Citation: Alexander Barg, Woomyoung Park, “On linear ordered codes”, Mosc. Math. J., 15:4 (2015), 679–702

Citation in format AMSBIB
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\by Alexander~Barg, Woomyoung~Park
\paper On linear ordered codes
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 679--702
\mathnet{http://mi.mathnet.ru/mmj580}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-679-702}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438827}
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