This article is cited in 3 papers

Fourth seminar to the memory of D.N. Klyshko

Algebraic solution of the synthesis problem for coded sequences

A. N. Leukhin

Mari State Technical University

Abstract: The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations for a given code dimension is solved. It is pointed out that the problem of synthesis of PC sequences is related to the fundamental problems of discrete mathematics and, first of all, to a number of combinatorial problems, which can be solved, as the number factorisation problem, by algebraic methods by using the theory of Galois fields and groups.

PACS: 03.67.Dd, 03.67.Lx

Received: 02.06.2005

 English version: Quantum Electronics, 2005, 35:8, 688–692

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