11,400 research outputs found
On diameter perfect constant-weight ternary codes
From cosets of binary Hamming codes we construct diameter perfect
constant-weight ternary codes with weight (where is the code length)
and distances 3 and 5. The class of distance 5 codes has parameters unknown
before. Keywords: constant-weight codes, ternary codes, perfect codes, diameter
perfect codes, perfect matchings, Preparata codesComment: 15 pages, 2 figures; presented at 2004 Com2MaC Conference on
Association Schemes, Codes and Designs; submitted to Discrete Mathematic
Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes
An optimal constant-composition or constant-weight code of weight has
linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or
constant-weight code is trivial, but the case of has been solved
previously only for binary and ternary constant-composition and constant-weight
codes, and for some sporadic instances.
This paper provides a construction for quasicyclic optimal
constant-composition and constant-weight codes of weight and distance
based on a new generalization of difference triangle sets. As a result,
the sizes of optimal constant-composition codes and optimal constant-weight
codes of weight and distance are determined for all such codes of
sufficiently large lengths. This solves an open problem of Etzion.
The sizes of optimal constant-composition codes of weight and distance
are also determined for all , except in two cases.Comment: 12 page
New Bounds for the Maximum Size of Ternary Constant Weight Codes
This work was partially supported by the Bulgarian National Science Fund under Grant I–618/96.Optimal ternary constant-weight lexicogarphic codes have been
constructed. New bounds for the maximum size of ternary constant-weight
codes are obtained. Tables of bounds on A3 (n, d, w) are given for d = 3, 4, 6
Symmetric Disjunctive List-Decoding Codes
A binary code is said to be a disjunctive list-decoding -code (LD
-code), , , if the code is identified by the incidence
matrix of a family of finite sets in which the union (or disjunctive sum) of
any sets can cover not more than other sets of the family. In this
paper, we consider a similar class of binary codes which are based on a {\em
symmetric disjunctive sum} (SDS) of binary symbols. By definition, the
symmetric disjunctive sum (SDS) takes values from the ternary alphabet , where the symbol~ denotes "erasure". Namely: SDS is equal to ()
if all its binary symbols are equal to (), otherwise SDS is equal
to~. List decoding codes for symmetric disjunctive sum are said to be {\em
symmetric disjunctive list-decoding -codes} (SLD -codes). In the
given paper, we remind some applications of SLD -codes which motivate the
concept of symmetric disjunctive sum. We refine the known relations between
parameters of LD -codes and SLD -codes. For the ensemble of binary
constant-weight codes we develop a random coding method to obtain lower bounds
on the rate of these codes. Our lower bounds improve the known random coding
bounds obtained up to now using the ensemble with independent symbols of
codewords.Comment: 18 pages, 1 figure, 1 table, conference pape
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