The Construction of Regular Hadamard Matrices by Cyclotomic Classes

Autor: Jennifer Seberry, Tianbing Xia, Mingyuan Xia
Rok vydání: 2020
Předmět:
Zdroj: Bulletin of the Iranian Mathematical Society. 47:601-625
ISSN: 1735-8515
1017-060X
DOI: 10.1007/s41980-020-00402-9
Popis: For every prime power $$q \equiv 7 \; mod \; 16$$ , there are (q; a, b, c, d)-partitions of GF(q), with odd integers a, b, c, and d, where $$a \equiv \pm 1 \; mod \; 8$$ such that $$q=a^2+2(b^2+c^2+d^2)$$ and $$d^2=b^2+2ac+2bd$$ . Many results for the existence of $$4-\{q^2; \; \frac{q(q-1)}{2}; \; q(q-2) \}$$ SDS which are simple homogeneous polynomials of parameters a, b, c and d of degree at most 2 have been found. Hence, for each value of q, the construction of SDS becomes equivalent to building a $$(q; \; a, \; b, \; c, \; d)$$ -partition. Once this is done, the verification of the construction only involves verifying simple conditions on a, b, c and d which can be done manually.
Databáze: OpenAIRE
Externí odkaz: