Event Details
Double Circulant Self-Dual Codes from Legendre Sequences
Presenter: Najme Sahami
Supervisor:
Date: Tue, July 30, 2024
Time: 10:00:00 - 00:00:00
Place: Zoom, link below.
ABSTRACT
Abstract:
A Legendre sequence s of length p, where p is an odd prime, is used to create a circulant matrix S. An alternative Legendre sequence, ˜s, is employed to form another circulant matrix ˜S. By concatenating these two matrices, we obtain the matrix D′, which is subsequently used to form a bordered double-circulant code with length 2p + 2 and dimension k = p + 1 over GF(q), q is a prime and gcd(p, q) = 1. We demonstrate that for p = 2qm − 1 the code generated by
D =11 1^t |1^t
10 S|˜S
over GF(q) is self-dual. We introduce the decomposition of these codes, emphasizing their self-dual properties. Theoretical proofs are provided to support the orthogonality and self-orthogonality of the rows of these codes. Additionally, we discuss the rank of the circulant matrices formed by Legendre sequences of length p = 4kq−1 over GF(q). We demonstrate that specific row-column permutations in D′ lead to non-singular matrices, revealing that these codes can be defined as direct sums of codes generated by S and ˜ S.
Time: Jul 30, 2024 10:00 AM Vancouver
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