Cuiling Fan

Linear codes with two or three weights from quadratic Bent functions

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of p-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field

Constructions of Difference Systems of Sets and Disjoint Difference Families

{\mathbb {F}}_p

Optimal difference systems of sets and partition-type cyclic difference packings

Fp, where p is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.

Constructions of Difference Systems of Sets From Finite Projective Geometry

Abstract Cyclic Reed–Solomon codes, a type of BCH codes, are widely used in consumer electronics, communication systems, and data storage devices. This fact demonstrates the importance of BCH codes – a family of cyclic codes – in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the narrow-sense primitive BCH codes. However, the dimension and minimum distance of these codes are not known in general. The objective of this paper is to determine the dimension and minimum distances of two classes of narrow-sense primitive BCH codes with designed distances δ = ( q − 1 ) q m − 1 − 1 − q ⌊ ( m − 1 ) / 2 ⌋ and δ = ( q − 1 ) q m − 1 − 1 − q ⌊ ( m + 1 ) / 2 ⌋ . The weight distributions of some of these BCH codes are also reported. As will be seen, the two classes of BCH codes are sometimes optimal and sometimes among the best linear codes known.

Two infinite classes of rotation symmetric bent functions with simple representation

Difference systems of sets (DSSs) are combinatorial structures that are a generalization of cyclic difference sets and arise in connection with code synchronization. In this correspondence, we give some constructions of DSS from cyclic designs and get some infinite classes of optimal difference systems of sets.

A Combinatorial Construction for Strictly Optimal Frequency-Hopping Sequences

The theory of cyclotomy dates back to Gauss and has a number of applications in combinatorics, coding theory, and cryptography. Cyclotomy over a residue class ring \BBZv can be divided into classical cyclotomy or generalized cyclotomy, depending on v prime or composite. In this paper, we introduce a generalized cyclotomy of order d over \BBZp1e1p2e2,..., pnen, which includes Whitemans and Ding-Helleseths generalized cyclotomy as special cases. Here, p1,p2,...,pn are pairwise distinct odd primes satisfying d|(pi-1) for all 1 ≤ i ≤ n and e1,e2,...,en are positive integers. We derive some basic properties of the corresponding cyclotomic numbers and obtain a general formula to compute them via classical cyclotomic numbers. As applications, we completely solve an open problem and a conjecture on Whitemans generalized cyclotomy of order four over \BBZp1p2. Besides, we also construct an infinite series of near-optimal codebooks over \BBZp1p2, as well as some infinite series of asymptotically optimal difference systems of sets over \BBZp1e1p2e2,...,pnen.

New optimal binary sequences with period 4p via interleaving Ding–Helleseth–Lam sequences

Difference systems of sets (DSSs) are combinatorial structures which were introduced by Levenshtein in connection with code synchronization. In this paper, we give some recursive constructions of DSSs by using partition-type cyclic difference packings, and obtain new infinite classes of optimal DSSs.

Unified combinatorial constructions of optimal optical orthogonal codes

Difference systems of sets (DSSs) are combinatorial structures introduced by Levenshtein in connection with code synchronization. In this paper, some recursive constructions of DSSs obtained from finite projective geometry are presented. As a consequence, new infinite families of optimal DSSs are obtained.