Abstract
Problems of search and enumeration of binary and ternary equidistant codes are considered in the paper. We investigate some combinatorial algorithms and develop specialized computer packages to find non-equivalent optimal binary and ternary equidistant codes for 3 ≤ d ≤ n ≤ 9.
Highlights
We can define a q-ary (n, M, d)q code as a set of M vectors with length n over the alphabet Zq = {0, 1, 2, . . . , q − 1} and with additional conditions that any two different vectors differ in at least d coordinates
If we add a restriction for all the codewords to have Hamming weight w, it becomes a constant weight
An (n, M, d)q equidistant code is a set of M codewords of length n over the alphabet {0, 1, . . . , q − 1}, and any two different codewords differ in exactly d positions
Summary
If Aq(n, d, w) indicates the biggest value M for an (n, M, d, w)q code, a code with parameters n, Aq(n, d, w), d, w q is considered optimal. More results about such codes can be found in [2,5,7,8]. We can define an equidistant constant weight code (n, M, d, w)q as a set of M codewords of length n over the alphabet {0, 1, . An equidistant constant weight with Bq(n, d, w) codewords is called optimal. There are two important problems in coding theory related to code generation and code enumeration up to equivalence.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
