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. https://resolver.caltech.edu/CaltechAUTHORS:20200323-144037642
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Abstract
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].
| Item Type: | Article | ||||||||||||
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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 | ||||||||||||
| DOI: | 10.1007/s10623-007-9076-3 | ||||||||||||
| Record Number: | CaltechAUTHORS:20200323-144037642 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200323-144037642 | ||||||||||||
| Official Citation: | Yildiz, B. Weights modulo pe of linear codes over rings. Des Codes Crypt 43, 147–165 (2007). https://doi.org/10.1007/s10623-007-9076-3 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 102059 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 23 Mar 2020 23:17 | ||||||||||||
| Last Modified: | 16 Nov 2021 18:08 |
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