Constructions of Polyphase Golay Complementary Arrays

20 Apr 2022  ·  , ·

Golay complementary matrices (GCM) have recently drawn considerable attentions owing to its potential applications in omnidirectional precoding. In this paper we generalize the GCM to multi-dimensional Golay complementary arrays (GCA) and propose new constructions of GCA pairs and GCA quads. These constructions are facilitated by introducing a set of identities over a commutative ring. We prove that a quaternary GCA pair is feasible if the product of the array sizes in all dimensions is a quaternary Golay number with an additional constraint on the factorization of the product. For the binary GCM quads, we conjecture that the feasible sizes are arbitrary, and verify for sizes within 78 $\times$ 78 and other less densely distributed sizes. For the quaternary GCM quads, all the positive integers within 1000 can be covered for the size in one dimension.

PDF Abstract

No code implementations yet. Submit your code now

Datasets

Add Datasets introduced or used in this paper

Results from the Paper Add Remove

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.