IJPAM: Volume 100, No. 3 (2015)
TWO-DIMENSIONAL LINEAR CODES
School of Information
Computer and Communication Technology
Sirindhorn International Institute of Technology
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 -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?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 391 - 403