Seven special cases which are presented were chosen from the simplest problems in signal detection which closely represent practical situations and should serve to suggest methods for attacking other simple signal detection problems and to give insight into problems too complicated to allow a direct solution.Expand

A simple error-correction procedure for binary codes which for arbitrary m and t are t -error correcting and have length 2^m - 1 of which no more than mt digits are redundancy is described.Expand

Estimates are made of the amount of searching required for the exact location of a record in several types of storage systems, including the index-table method of addressing and the sorted-file… Expand

A number of results on minimum weights in BCH codes are presented, and exact minimum weights have been established for a number of subclasses of NBCH codes.Expand

A natural generalization to the nonbinary case is presented, which also includes the Reed-Muller codes and Reed-Solomon codes as special cases and the generator polynomial is characterized and the minimum weight is established.Expand

The potentialities of these codes for error detection and the equipment required for implementing error detection systems using cyclic codes are described in detail.Expand

A class of linear error-correcting block codes is investigated and it is shown that an important subclass of the class of cyclic codes is almost equivalent to quasicyclic codes.Expand

A class of cyclic codes is introduced by a polynomial approach that is an extension of the Mattson-Solomon method and of the Muller method and some subclasses are shown to be majority-logic decodable.Expand

It is shown that all two-error correcting Bose-Chaudhuri codes are close-packed and therefore optimum. A method is also given for finding cosets of large weight in t > 2-error correcting… Expand