The Existence of Optimal (v,4,1) Optical Orthogonal Codes Achieving the Johnson Bound

Abstract

Optical orthogonal codes have applications in optical code-division multiple access communication systems. They can also be used to construct protocol sequences for multiuser collision channel without feedback, and constant weight codes for error detection and correction. Direct constructions with explicit codewords are presented to settle the existence of a J-optimal $(v,4,1)$ -optical orthogonal code with $\lfloor (v-1)/12\rfloor $ codewords for any positive integer $v\neq 25$ . As a corollary, it is shown that an optimal $(v,6,4)$ -cyclically permutable constant weight code with $\lfloor (v-1)/12\rfloor $ codewords exists for any positive integer $v\neq 25$ .