Group symmetries of complementary code matrices

Brooke Logan; Hieu D. Nguyen

doi:10.1109/TAES.2016.150478

Group symmetries of complementary code matrices

Brooke Logan, Hieu D. Nguyen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Complementary code matrices (CCMs) generalize Golay pairs and Hadamard matrices. In this paper, we describe new group relations satisfied by CCM-preserving symmetries and use its symmetry group to classify CCMs in terms of their equivalence classes. We also give an upper bound on the order of this group, determine the number of equivalence classes of N × 4 quad-phase CCMs where N = 2, 3, 4, 5, 6, and present a new construction to generate quad-phase CCMs from ternary CCM dual pairs.

Original language	English (US)
Article number	7812875
Pages (from-to)	2255-2262
Number of pages	8
Journal	IEEE Transactions on Aerospace and Electronic Systems
Volume	52
Issue number	5
DOIs	https://doi.org/10.1109/TAES.2016.150478
State	Published - Oct 2016

All Science Journal Classification (ASJC) codes

Aerospace Engineering
Electrical and Electronic Engineering

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10.1109/TAES.2016.150478

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AB - Complementary code matrices (CCMs) generalize Golay pairs and Hadamard matrices. In this paper, we describe new group relations satisfied by CCM-preserving symmetries and use its symmetry group to classify CCMs in terms of their equivalence classes. We also give an upper bound on the order of this group, determine the number of equivalence classes of N × 4 quad-phase CCMs where N = 2, 3, 4, 5, 6, and present a new construction to generate quad-phase CCMs from ternary CCM dual pairs.

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Group symmetries of complementary code matrices

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