TY - JOUR
T1 - Near-complete external difference families
AU - Davis, James A.
AU - Huczynska, Sophie
AU - Mullen, Gary L.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.
AB - We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.
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U2 - 10.1007/s10623-016-0275-7
DO - 10.1007/s10623-016-0275-7
M3 - Article
AN - SCOPUS:84984797679
SN - 0925-1022
VL - 84
SP - 415
EP - 424
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 3
ER -