Generalized construction of two-dimensional complete complementary codes

Abstract

Farkaš and Turcsány proposed construction method of two-dimensional (2D) complete complementary codes (CCC) with element order N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This construction is based on one-dimensional (1D) CCC introduced by Suehiro with element length N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . New constructions of CCC with shorter 1D-CCC element lengths were published recently. In this paper former construction of 2D-CCC is generalized for using any recent 1D-CCC for input which results in 2D-CCC with element of smaller order. Dependences of code parameters of 2D code on 1D code parameters are discussed. Advantage of smaller element order enables higher channel efficiency and thus higher transmission rates and capacity. Usage of 2D-CCC codes enables diversity.