Further Results on Error Correcting Binary Group Codes

The present paper is a sequel to the paper “On a class of error-correcting binary group codes”, by R. C. Base and D. K. Ray-Chaudhuri, appearing in Information and Control in which an explicit method of constructing a t-error correcting binary group code with n = 2m − 1 places and k = 2m − 1 − R(m,t) ≧ 2m − 1 − mt information places is given. The present paper generalizes the methods of the earlier paper and gives a method of constructing a t-error correcting code with n places for any arbitrary n and k = n − R(m,t) ≧ [(2m − 1)/c] − mt information places where m is the least integer such that cn = 2m − 1 for some integer c. A second method of constructing t-error correcting codes for n places when n is not of the form 2m − 1 is also given.