If D is a (4u2, 2u2 − u, u2 − u) Hadamard difference set (HDS) in G, then {G,G D} is clearly a (4u2, [2u2 − u, 2u2 + u], 2u2) partitioned difference family (PDF). Any (v,K, λ)-PDF will be said a Hadamard PDF if v = 2λ as the one above. We present a doubling construction which, starting from any Hadamard PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order 4u2(2n + 1) and three block-sizes 4u2 − 2u, 4u2 and 4u2 + 2u, whenever we have a (4u2, 2u2 − u, u2 − u)-HDS and the maximal prime power divisors of 2n + 1 are all greater than 4u2 + 2u.
Hadamard partitioned difference families and their descendants / Buratti, Marco. - In: CRYPTOGRAPHY AND COMMUNICATIONS. - ISSN 1936-2447. - 11:4(2019), pp. 557-562. [10.1007/s12095-018-0308-3]
Hadamard partitioned difference families and their descendants
Marco Buratti
2019
Abstract
If D is a (4u2, 2u2 − u, u2 − u) Hadamard difference set (HDS) in G, then {G,G D} is clearly a (4u2, [2u2 − u, 2u2 + u], 2u2) partitioned difference family (PDF). Any (v,K, λ)-PDF will be said a Hadamard PDF if v = 2λ as the one above. We present a doubling construction which, starting from any Hadamard PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order 4u2(2n + 1) and three block-sizes 4u2 − 2u, 4u2 and 4u2 + 2u, whenever we have a (4u2, 2u2 − u, u2 − u)-HDS and the maximal prime power divisors of 2n + 1 are all greater than 4u2 + 2u.File | Dimensione | Formato | |
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