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Weights modulo p^e of linear codes over rings

Yildiz, Bahattin (2007) Weights modulo p^e of linear codes over rings. Designs, Codes and Cryptography, 43 (2-3). pp. 147-165. ISSN 0925-1022. doi:10.1007/s10623-007-9076-3.

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In this paper we look at linear codes over the Galois ring GR(p^ℓ,m) with the homogeneous weight and we prove that the number of codewords with homogenous weights in a particular residue class modulo p^e are divisible by high powers of p. We also state a result for a more generalized weight on linear codes over Galois rings. We obtain similar results for the Lee weights of linear codes over F₂m+uF₂m and we prove that the results we obtain are best possible. The results that we obtain are an improvement to Wilson’s results in [Wilson RM (2003) In: Proceedings of international workshop on Cambridge linear algebra and graph coloring].

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Additional Information:© 2007 Springer Science+Business Media, LLC. Received 14 June 2006; Revised 28 March 2007; Accepted 02 April 2007; Published 16 May 2007. This paper is dedicated to my advisor Dr Richard M Wilson. The work presented here was part of the author’s thesis at Caltech under the supervision of Dr Richard Wilson.
Subject Keywords:Linear codes; Galois rings; Homogeneous weights; Lee weights
Issue or Number:2-3
Classification Code:AMS: 94B05; 11T71; 68P30
Record Number:CaltechAUTHORS:20200323-144037642
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Official Citation:Yildiz, B. Weights modulo pe of linear codes over rings. Des Codes Crypt 43, 147–165 (2007).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102059
Deposited By: Tony Diaz
Deposited On:23 Mar 2020 23:17
Last Modified:16 Nov 2021 18:08

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