10 research outputs found
Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
The concept of group divisible codes, a generalization of group divisible
designs with constant block size, is introduced in this paper. This new class
of codes is shown to be useful in recursive constructions for constant-weight
and constant-composition codes. Large classes of group divisible codes are
constructed which enabled the determination of the sizes of optimal
constant-composition codes of weight three (and specified distance), leaving
only four cases undetermined. Previously, the sizes of constant-composition
codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table
Importance of Symbol Equity in Coded Modulation for Power Line Communications
The use of multiple frequency shift keying modulation with permutation codes
addresses the problem of permanent narrowband noise disturbance in a power line
communications system. In this paper, we extend this coded modulation scheme
based on permutation codes to general codes and introduce an additional new
parameter that more precisely captures a code's performance against permanent
narrowband noise. As a result, we define a new class of codes, namely,
equitable symbol weight codes, which are optimal with respect to this measure
A Construction for Constant-Composition Codes
By employing the residue polynomials, a construction of constant-composition
codes is given. This construction generalizes the one proposed by Xing[16]. It
turns out that when d=3 this construction gives a lower bound of
constant-composition codes improving the one in [10]. Moreover, for d>3, we
give a lower bound on maximal size of constant-composition codes. In
particular, our bound for d=5 gives the best possible size of
constant-composition codes up to magnitude.Comment: 4 pages, submitted to IEEE Infromation Theor
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
The PBD-Closure of Constant-Composition Codes
We show an interesting PBD-closure result for the set of lengths of
constant-composition codes whose distance and size meet certain conditions. A
consequence of this PBD-closure result is that the size of optimal
constant-composition codes can be determined for infinite families of parameter
sets from just a single example of an optimal code. As an application, the size
of several infinite families of optimal constant-composition codes are derived.
In particular, the problem of determining the size of optimal
constant-composition codes having distance four and weight three is solved for
all lengths sufficiently large. This problem was previously unresolved for odd
lengths, except for lengths seven and eleven.Comment: 8 page