Lower bounds on cross-correlation of codes
V.I. Levenshtein · 2002
Codes with low cross-correlation are broadly used in code-division multiple-access (CDMA) communication systems. In this paper the best known lower bounds on the cross-correlation of real and complex codes of a given size obtained by the author in 1982 are investigated. For some range of parameters these bounds are strengthened. Their optimality in the framework of the linear programming method for polynomials of restricted degree is proved. New asymptotics, when the size of codes grows as a degree of length, are given. It is shown that the best known lower bounds on cross-correlation of binary and /spl nu/-ary codes (/spl nu//spl ges/3) have the same asymptotic behaviour as ones for real and complex codes respectively when the code rate tends to zero.