Naslov
On equivalence of negaperiodic Golay pairs

Autori
Egan, Ronan

Izvornik
Designs, codes and cryptography (0925-1022) 85 (2017), 3; 523-532

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Negaperiodic Golay pair ; Hadamard matrix ; Relative difference set ; Binary sequences
(Negaperiodic Golay pair ; Hadamard matrix ; Relative differen)

Sažetak
Associated pairs as defined by Ito (J Algebra 234:651–663, 2000) are pairs of binary sequence of length 2t satisfying certain autocorrelation properties that may be used to construct Hadamard matrices of order 4t. More recently, Balonin and Doković (Inf Control Syst 5:2–17, 2015) use the term negaperiodic Golay pairs. We define extended negaperiodic Golay pairs and prove a one-to-one correspondence with central relative (4t, 2, 4t, 2t)-difference sets in dicyclic groups of order 8t. We present a new approach for computing negaperiodic Golay pairs up to equivalence, and determine conditions where equivalent pairs correspond to equivalent Hadamard matrices. We complete an enumeration of negaperiodic Golay pairs of length 2t for 1≤t≤10, and sort them into equivalence classes. Some structural properties of negaperiodic Golay pairs are derived.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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