A Simple Method For, Generation Of A Class Of Superimposed Codes

Abstract

A b s t r a c t -A set C of vectors over Rn is said to be a superimposed code of order m and distance d if it has the property that, for some positive integer m and some positive real number d, all sums of up to m vectors from C are separated by at least distance d. Superimposed codes can be used in multipleaccess communication to ensure that communication is possible even when several users want simultaneous access to the channel. Our interest lies in finding superimposed codes for the Euclidpan channel.A B,-sequence is a set of integers such that all sums of s elements are distinct. It has been shown that a B,-sequence can be transformed into a superimposed code. Here we show that B,-sequences can be generated by m-sequences obtained from linear-feedback shift registers. Superimposed codes in R"Let C be a set of T unit norm vectors in R". Let the vectors x = (zl,. . . , zn) and y = (yl,. . . ,yn) be sums of vectors from C, and let the distance between x and y be dE(Z,Y) 2 IIZ -3111 = c (G -Y r Y