On the extended Lee weights modulo 2e of linear codes over Z2.

Bahattin Yildiz; Zeynep Ödemiş Özger

On the extended Lee weights modulo 2^e of linear codes over Z₂.

Bahattin Yildiz, Zeynep Ödemiş Özger

Research output: Contribution to journal › Article › peer-review

Abstract

In this work, lineax codes over Z₂ are considered together with the extended Lee weight that is defined as (Equation presented) The ideas used by Wilson and Yildiz are employed to obtain divisibility properties for sums involving binomial coefficients and the extended Lee weight. These results are then used to find bounds on the power of 2 that divides the number of codewords whose Lee weights fall in the same congruence class modulo 2^e. Comparisons are made with the results for the trivial code and the results for the homogeneous weight.

Original language	English (US)
Pages (from-to)	289-302
Number of pages	14
Journal	Ars Combinatoria
Volume	130
State	Published - Jan 2017
Externally published	Yes

Keywords

Codes over rings
Enumerators
Gray map
Linear codes

ASJC Scopus subject areas

General Mathematics

Cite this

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N2 - In this work, lineax codes over Z2 are considered together with the extended Lee weight that is defined as (Equation presented) The ideas used by Wilson and Yildiz are employed to obtain divisibility properties for sums involving binomial coefficients and the extended Lee weight. These results are then used to find bounds on the power of 2 that divides the number of codewords whose Lee weights fall in the same congruence class modulo 2e. Comparisons are made with the results for the trivial code and the results for the homogeneous weight.

AB - In this work, lineax codes over Z2 are considered together with the extended Lee weight that is defined as (Equation presented) The ideas used by Wilson and Yildiz are employed to obtain divisibility properties for sums involving binomial coefficients and the extended Lee weight. These results are then used to find bounds on the power of 2 that divides the number of codewords whose Lee weights fall in the same congruence class modulo 2e. Comparisons are made with the results for the trivial code and the results for the homogeneous weight.

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KW - Enumerators

KW - Gray map

KW - Linear codes

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On the extended Lee weights modulo 2^e of linear codes over Z₂.

Abstract

Keywords

ASJC Scopus subject areas

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