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 i...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.展开更多
Double Toeplitz(shortly DT)codes are introduced here as a generalization of double circulant codes.The authors show that such a code is isodual,hence formally self-dual(FSD).FSD codes form a far-reaching generalizatio...Double Toeplitz(shortly DT)codes are introduced here as a generalization of double circulant codes.The authors show that such a code is isodual,hence formally self-dual(FSD).FSD codes form a far-reaching generalization of self-dual codes,the most important class of codes of rate one-half.Self-dual DT codes are characterized as double circulant or double negacirculant.Likewise,even binary DT codes are characterized as double circulant.Numerical examples obtained by exhaustive search show that the codes constructed have best-known minimum distance,up to one unit,amongst formally self-dual codes,and sometimes improve on the known values.For q=2,the authors find four improvements on the best-known values of the minimum distance of FSD codes.Over F4 an explicit construction of DT codes,based on quadratic residues in a prime field,performs equally well.The authors show that DT codes are asymptotically good over Fq.Specifically,the authors construct DT codes arbitrarily close to the asymptotic Varshamov-Gilbert bound for codes of rate one half.展开更多
To solve the problem of low efficiency in pipe routing design, an improved genetic algorithm based approach is proposed. To present this approach, the paper mainly describes a generation method of nodes considering th...To solve the problem of low efficiency in pipe routing design, an improved genetic algorithm based approach is proposed. To present this approach, the paper mainly describes a generation method of nodes considering the safety distance of pipes and the directional constraints at terminals, the definition of a double coding technique, the collision detection method, the concept of energy and the definition of fitness functions. The similarity detection is introduced to prevent close breeding in the crossover operator, the selection pressure is controlled according to the evolution situation and a heuristic mutation method is used to boost the evolution. Simulation case shows that this approach is more practical and can satisfy different design requirements by changing algorithm parameters.展开更多
文摘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.
基金supported by the National Natural Science Foundation of China under Grant No.12071001。
文摘Double Toeplitz(shortly DT)codes are introduced here as a generalization of double circulant codes.The authors show that such a code is isodual,hence formally self-dual(FSD).FSD codes form a far-reaching generalization of self-dual codes,the most important class of codes of rate one-half.Self-dual DT codes are characterized as double circulant or double negacirculant.Likewise,even binary DT codes are characterized as double circulant.Numerical examples obtained by exhaustive search show that the codes constructed have best-known minimum distance,up to one unit,amongst formally self-dual codes,and sometimes improve on the known values.For q=2,the authors find four improvements on the best-known values of the minimum distance of FSD codes.Over F4 an explicit construction of DT codes,based on quadratic residues in a prime field,performs equally well.The authors show that DT codes are asymptotically good over Fq.Specifically,the authors construct DT codes arbitrarily close to the asymptotic Varshamov-Gilbert bound for codes of rate one half.
基金Supported by National "863" Project of China (2006AA09A104)
文摘To solve the problem of low efficiency in pipe routing design, an improved genetic algorithm based approach is proposed. To present this approach, the paper mainly describes a generation method of nodes considering the safety distance of pipes and the directional constraints at terminals, the definition of a double coding technique, the collision detection method, the concept of energy and the definition of fitness functions. The similarity detection is introduced to prevent close breeding in the crossover operator, the selection pressure is controlled according to the evolution situation and a heuristic mutation method is used to boost the evolution. Simulation case shows that this approach is more practical and can satisfy different design requirements by changing algorithm parameters.
