Q-ary gray codes and weight distributions
Applied Mathematics and Computation
Optimal quaternary linear codes of dimension five
IEEE Transactions on Information Theory
Optimal linear codes of dimension 4 over F5
IEEE Transactions on Information Theory
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Extremal self-dual codes with an automorphism of order 2
IEEE Transactions on Information Theory
Some new extremal self-dual codes with lengths 44, 50, 54, and 58
IEEE Transactions on Information Theory
On the inherent intractability of certain coding problems (Corresp.)
IEEE Transactions on Information Theory
A probabilistic algorithm for computing minimum weights of large error-correcting codes
IEEE Transactions on Information Theory - Part 1
New results on s-extremal additive codes over GF(4)
International Journal of Information and Coding Theory
On quantum information and the protection by quantum codes
Proceedings of the 11th International Conference on Computer Systems and Technologies and Workshop for PhD Students in Computing on International Conference on Computer Systems and Technologies
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The problem of computing the number of codewords of weights not exceeding a given integer in linear codes over a finite field is considered. An efficient method for solving this problem is proposed and discussed in detail. It builds and uses a sequence of different generator matrices, as many as possible, so that the identity matrix takes disjoint places in them. The efficiency of the method is achieved by optimizations in three main directions: (1) the number of the generated codewords, (2) the check whether a given codeword is generated more than once, and (3) the operations for generating and computing these codewords. Since the considered problem generalizes the well-known problems ''Weight Distribution'' and ''Minimum Distance'', their efficient solutions are considered as applications of the algorithms from the method.