Algorithmic complexity in coding theory and the minimum distance problem

Alexander Vardy
1997 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97  
We start withan overviewof algorithmiccomplexity problemsin coding theory We then show that the problemof computing the minimumdiktanceof a binaryIinwr code is NP-hard,and the corresponding deci~"on problemis W-complete. This constitutes a proof of the conjecture Bedekamp, McEliece,vanTilborg, dating back to 1978. Extensionsand applicationsof this result to other problemsin codingtheqv are discussed.
doi:10.1145/258533.258559 dblp:conf/stoc/Vardy97 fatcat:vkunvltuabfdvnjzldvt6mpihu