Some Constructions of T -Direct Codes over GF(2n)

Abstract

The class of T -Direct codes are an extension to the class of linear codes with complementary duals. In this paper, a construction procedure that constructs an n2-Direct code from an n-Direct code is described. Further, the construction procedure is employed recursively to construct n2m+1 -Direct codes for m ≥ 0. Finally, T 2-Direct codes are obtained from arbitraryT -Direct codes with constituent codes of variable rates. The proposed construction procedure, when employed on an existingT -Direct code, in fact increases the number of constituent codes (users), thereby supporting more users in a multi-user environment.