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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Inequivalence of Nega-cyclic \(\pm 1\) Matrices

Russeli Ang1, Jennifer Seberry1, Tadeusz Wysocki2
1Centre for Computer Security Research, School of IT and Computer Science
2School of Electrical, Computer and Telecommunications Engineering, University of Wollongong NSW 2522 Australia
  • Published: 28/02/2006

Abstract

We study nega-cyclic \(\pm 1\) matrices. We obtain preliminary results which are then used to decrease the search space. We find that there are \( 2 \), \( 4 \), \( 9 \), \( 23 \), \( 63 \), and \( 187 \) ip-equivalence classes for lengths \( 3 \), \( 5 \), \( 7 \), \( 9 \), \( 11 \), and \( 13 \) respectively. The matrices we find are used in a variant given here of the Goethals-Seidel array to form Hadamard matrices, the aim being to later check them for suitability for CDMA schemes.

Keywords: Hadamard matrix, nega-cyclic, ip-equivalence classes, Goethals-Seidel array, variant Goethals-Seidel array AMS Subject Classification: Primary 05B20, Secondary 62K05, 62K10
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Citation
Russeli Ang, Jennifer Seberry, Tadeusz Wysocki. Inequivalence of Nega-cyclic \(\pm 1\) Matrices[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 056. 17-32. DOI: .