Abstract
Kasami and Lin [l] have developed a method to construct a class of two-user Mecodable codes (Cl, 62) which are called linear in the sense that they satisfy the following two conditions: (1) One component code, say Ci, is linear. (2) There exists a linear code C with minimum Hamming distance at least 6 such that C contains Ci U a. These facilitate the design of a simple decoder for codes of this type. However, condition (2) gives much restriction in finding good codes of this type. We relax condition (2) and shows that a simple decoder still exists for such a wider class of codes. Codes with high rate can be constructed by a proposed graph theoretical method, similar to that in Kasami, Lin, Wei, and Yamamura [2]. We extend these results further to give two different constructions of three-user codes. Good codes have been searched out and simple decoding algorithms are develoDed.