New Bounds and Constructions for Constant Weighted X-Codes

As a crucial technique for integrated circuits (IC) test response compaction, X-compact employs special kind of codes called X-codes reliable compressions the in presence unknown logic values (Xs). From combinatorial view point, Fujiwara and Colbourn introduced an equivalent definition studied small weights that have good detectability X-tolerance. An ( m , xmlns:xlink="http://www.w3.org/1999/xlink">n xmlns:xlink="http://www.w3.org/1999/xlink">d xmlns:xlink="http://www.w3.org/1999/xlink">x ) X-code is m× n binary matrix with column vectors as its codewords. The parameters correspond to quality code. In this paper, bounds constructions constant weighted are investigated. First, we obtain general result on maximum number codewords weight w, further improve lower bound case x=2 w=3 through probabilistic method. Then, using tools from additive combinatorics finite fields, present some explicit d=3,7 x=2, which optimal when d=3, w=4 nearly w=3. We also consider class by best known X-codes.