Abstract
In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w < n ≤ 10. Computer search of lexicographic constant-weight equidistant codes is performed. Tables with bounds on the size of lexicographic constant-weight equidistant codes are presented.
Highlights
Consider a finite set of q elements and containing a distinguished element “zero”
Lexicographic codes of length n and Hamming distance d are obtained by considering all q-ary vectors with weight w in lexicographic order, and adding them to the code if they are at a distance exactly d from the words that have been added earlier
In order to find lexicographic codes we can start the search in the following ways: Without seeds: As a result, we construct lexicographic code where the first codeword is the first word in the set of vectors Z qn ; With seeds: In this case, it is important to choose a proper seed from one or more vectors
Summary
Consider a finite set of q elements and containing a distinguished element “zero”. The choice of a set does not matter in our context and we will use the set Z q of integers modulo q. A few papers study codes which are both equidistant and of constant. Lexicographic codes of length n and Hamming distance d are obtained by considering all q-ary vectors with weight w in lexicographic order, and adding them to the code if they are at a distance exactly d from the words that have been added earlier. In the present paper is considered the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements.
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