منابع مشابه
Difference families from rings
Furino, S., Difference families from rings, Discrete Mathematics 97 (1991) 177-190. Some difference family constructions originating with Bose, Hanani and Wilson that require finite fields are modified to work in rings with unity. These ring constructions are then used to derive new classes of abelian and cyclic difference families with blocks size 4. These constructions are also used to provid...
متن کاملDisjoint Difference Families from Galois Rings
In this paper, we give new constructions of disjoint difference families from Galois rings. The constructions are based on choosing cosets of the unit group of a subring in the Galois ring GR(p2, p2s). Two infinite families of disjoint difference families are obtained from the Galois rings GR(p2, p4n) and GR(22, 22s).
متن کاملDivisible difference families from Galois rings GR(4, n) and Hadamard matrices
We give a new construction of difference families generalizing Szekeres’s difference families [17]. As an immediate consequence, we obtain some new examples of difference families with several blocks in multiplicative subgroups of finite fields. We also prove that there exists an infinite family of divisible difference families with two blocks in a unit subgroup of the Galois ring GR(4, n). Fur...
متن کاملQuasi-cyclic LDPC codes from difference families
We consider in this paper regular and nearly regular quasi-cyclic low-density paritycheck (LDPC) codes, derived from families of difference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding.
متن کاملNew 2-designs from strong difference families
Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to 2-designs, and have applications in constructions for many significant codes, such as optical orthogonal codes and optical orthogonal signature pattern codes. In this paper, with a careful use of cyclotomic condi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90433-3