A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximu...
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A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the q-ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes the Graham-Sloane bound for binary constant-weight codes. In addition, three construction methods of constant-composition codes are presented, and a number of optimum constant-composition codes are obtained by using these constructions.
A concept of good overlarge set of disjoint packing triple systems (OLPTS) is introduced in order to characterize a ternary constant-composition code with weight four, distance three and the composition [3, 1]. A recu...
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A concept of good overlarge set of disjoint packing triple systems (OLPTS) is introduced in order to characterize a ternary constant-composition code with weight four, distance three and the composition [3, 1]. A recursive construction for good OLPTSs via fan designs is also given. 4-cycle free one-factorizations of the complete graphs are also used to construct optimal ternary constant-composition codes with weight four distance three and the composition [2, 2]. Consequently, a few infinite classes of optimal ternary constantcompositioncodes with weight four and distance three are obtained. (C) 2019 Elsevier B.V. All rights reserved.
Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type g (t) u (1) and establish that its necessary conditions are also suffic...
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Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type g (t) u (1) and establish that its necessary conditions are also sufficient.
As an optimal combinatorial object, zero-difference balanced (ZDB) functions introduced by Ding in 2008, are a generalization of the well-known perfect nonlinear functions. ZDB functions have received much attention i...
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As an optimal combinatorial object, zero-difference balanced (ZDB) functions introduced by Ding in 2008, are a generalization of the well-known perfect nonlinear functions. ZDB functions have received much attention in recent years due to its important applications in coding theory and sequence design. One objective of this paper is to present a construction of ZDB functions based on a kind of generalized cyclotomy. It generates ZDB functions over cyclic group with new parameters which can not be produced by earlier constructions. Another objective of this paper is to employ these ZDB functions to obtain at the same time: 1) optimal constant-composition codes;2) perfect difference systems of sets;and 3) optimal frequency-hopping sequences, all with new parameters.
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