IJPAM: Volume 100, No. 3 (2015)


Pramote Jangisarakul$^1$, Chalie Charoenlarpnopparut$^2$
$^{1,2}$School of Information
Computer and Communication Technology
Sirindhorn International Institute of Technology
Thammasat University
Klong Luang, Pathum-Thani 12121, THAILAND

Abstract. The tools of algebraic approach are used to decode two-dimensional linear block code defined as a two-step operation, namely a column-wise encoding matrix and a row-wise encoding matrix. A binomial ideal is essential to initiate the decoding algorithm associated with the Gröbner basis of this ideal and a $m$-variate division algorithm. To demonstrate the efficiency of the decoding process by using this algorithm can be measured in terms of the correctable percentage with interesting parameters: bit error probability, term ordering, and computational time. By testing erroneous bits in received codewords for several different encoding matrices of 2-D linear block codes, the algorithm can be reliable to correct up error-correcting capability of code. There is a struggle of several variables (indeterminates) in the binomial ideal since almost computational time will be lost finding Gröbner basis of binomial ideal.

Received: December 18, 2014

AMS Subject Classification: 94B05, 94B35

Key Words and Phrases: Groebner bases, linear block codes, decoding matrix

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DOI: 10.12732/ijpam.v100i3.6 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 100
Issue: 3
Pages: 391 - 403

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