Nonlinear Binary Codes Derived from Constacyclic Codes

This paper presents theorems showing how to obtain a binary nonlinear code from a p-ary linear constacyclic maximum distance separable code, where p is a prime number, by using a representation of GF(p) as binary ptuples. Two asymptotically optimum classes of binary constantweight codes are constructed. Binary cyclic codes are derived for a representation of GF(p) as (p-1)-tuples. It is shown for Mersenne primes p greater than 3 that all p-ary codewords of these codes have full constacyclic order. An application of some of the cyclically permutable codes constructed is given as an example of the construction of protocol sequences for the M-active-out-of-T users collision channel without feedback introduced by Massey.