Local search optimisation applied to the minimum distance problem

Bland, J. A.

doi:10.1016/j.aei.2007.01.002

Cited by 23 publications

(21 citation statements)

References 11 publications

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“…With α set to 1, we tested our algorithm on the set of 20 test cases given in six previous publications [4,13,8,5,7,24]. The heuristic search algorithms used in these publications are Wallis's GA [4,13], Askali's GA [4,5], Tabu-search [4,13,8,5], Hill Climbing [4,13,5], Ant colony optimization [7] and simulated annealing [7,24]. Each of these heuristics use the same set, namely, the set of all length k binary words, as their search space.…”

Section: Resultsmentioning

confidence: 99%

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Performance of metropolis algorithm for the minimum weight code word problem

Shenoy

Biswas

Kurur

2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M , given a generator matrix of an [n, k]-binary linear code. The algorithm uses the set S k of all k × k invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T . We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

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Section: Resultsmentioning

confidence: 99%

“…It is for this reason that researchers have proposed several probabilistic and heuristic algorithms to find low weight code words, given a basis of a binary linear code. Examples are: GA [4,13,5], hill climbing [4,13,5], tabu search [8], and ACO [7].…”

Section: Introductionmentioning

confidence: 99%

Performance of metropolis algorithm for the minimum weight code word problem

Shenoy

Biswas

Kurur

2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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“…In order to validate the proposed method, it is applied on all QR codes of known minimum distance presented in [14][15][16][17][18][19][20][21]. The TABLE I summarizes the obtained results, it shows that the minimum weight found by the Zimmermann-FSI method is equal to the true value of the minimum distance of all QR codes of known minimum distance.…”

Section: Validation Of Zimmermann-fsi Methodmentioning

confidence: 98%

“…When the dimension k increases, the size of the search space becomes prohibitively large and exhaustive search becomes not feasible. In [14][15][16][17][18][19][20][21] authors have used many techniques to find the true value of the minimum distances of QR codes for all lengths less than or equal to 223. For more lengths, this metric is still unknown.…”

Section: Related Workmentioning

confidence: 99%

New efficient techniques to catch lowest weights in large Quadratic Residue codes

Namir¹,

Abderrahman²,

Nouh³

2017

Fifth International Conference on Advances in Computing, Electronics and Communication - ACEC 2017

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“…They achieved important improvement with the inclusion of the RA. In a related context, the authors of [9] resolved the question of the utility of the crossover operator in earlier studies on optimizing DNA error correcting codes, where the crossover operator in question was found to be substantially counterproductive and the majority of the crossover events produced results that violated the minimum distance constraints required for error correction.…”

Section: Literature Reviewmentioning

confidence: 99%

Maximally Distant Codes Allocation Using Chemical Reaction Optimization with Enhanced Exploration

Eldos¹,

Khreishah²

2016

ijacsa

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Abstract-Error correcting codes, also known as error controlling codes, are sets of codes with redundancy that provides for error detection and correction, for fault tolerant operations like data transmission over noisy channels or data retention using storage media with possible physical defects. The challenge is to find a set of m codes out of 2 n available n-bit combinations, such that the aggregate hamming distance among those codewords and/or the minimum distance is maximized. Due to the prohibitively large solution spaces of practically sized problems, greedy algorithms are used to generate quick and dirty solutions. However, modern evolutionary search techniques like genetic algorithms, swarm particles, gravitational search, and others, offer more feasible solutions, yielding near optimal solutions in exchange for some computational time. The Chemical Reaction Optimization (CRO), which is inspired by the molecular reactions towards a minimal energy state, emerged recently as an efficient optimization technique. However, like the other techniques, its internal dynamics are hard to control towards convergence, yielding poor performance in many situations. In this research, we proposed an enhanced exploration strategy to overcome this problem, and compared it with the standard threshold based exploration strategy in solving the maximally distant codes allocation problem. Test results showed that the enhancement provided better performance on most metrics.

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Local search optimisation applied to the minimum distance problem

Cited by 23 publications

References 11 publications

Performance of metropolis algorithm for the minimum weight code word problem

Performance of metropolis algorithm for the minimum weight code word problem

New efficient techniques to catch lowest weights in large Quadratic Residue codes

Maximally Distant Codes Allocation Using Chemical Reaction Optimization with Enhanced Exploration

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