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An algebraic approach for decoding spread codes


Gorla, E; Manganiello, F; Rosenthal, J (2012). An algebraic approach for decoding spread codes. Advances in Mathematics of Communication, 6(4):443-466.

Abstract

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size k×n with entries in a finite field Fq. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires O((n−k)k3) operations over an extension field Fqk. Our algorithm is more efficient than the previous ones in the literature, when the dimension k of the codewords is small with respect to n. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields.

Abstract

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size k×n with entries in a finite field Fq. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires O((n−k)k3) operations over an extension field Fqk. Our algorithm is more efficient than the previous ones in the literature, when the dimension k of the codewords is small with respect to n. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:November 2012
Deposited On:25 Jan 2013 15:22
Last Modified:05 Apr 2016 16:20
Publisher:American Institute of Mathematical Sciences
ISSN:1930-5338
Additional Information:First published in Advances in Mathematics of Communication in Volume 6, No. 4, 2012, published by the American Institute of Mathematical Sciences and Shandong University.
Publisher DOI:https://doi.org/10.3934/amc.2012.6.443

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