Abstract
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call "Multiple Impulse Method (MIM)", where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.
Highlights
The Minimum distance of a linear error correcting code has a practical and theoretical interest
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms
The second approach is based on a new randomized algorithm which we call “Multiple Impulse Method (MIM)”, where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code
Summary
The Minimum distance of a linear error correcting code has a practical and theoretical interest It provides a great deal of information on the code capability in detecting and in correcting errors or erasures. We propose several different algorithms and heuristic search techniques such as Genetic Algorithm (GA) [1,2,3,4], and search local error using a Soft-In decoder when applied to the problem of determining the true minimum distance of a linear block code [5]. We deal with finding a good estimate of minimum distance of linear block codes using genetic algorithms to BCH, QR, and DCC codes and which we denote dt, and we compare our results to previous works.
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