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Distance bounds for constacyclic codes
Organisatsiooni nimiCoding and Information Transmission Group
KokkuvõteConstacyclic codes are a not much studied generalization of cyclic codes. A linear code C of length n over a finite field F_q is a-constacyclic if for every code word c=(c_0, c_1, ..., c_{n-1}) from C, the word (ac_{n-1}, c_0, c_1, ..., c_{n-2}) is again in C. (Cyclic codes are the case where a=1; and in fact, an a-constacyclic code is an ideal in F_q[x] mod x^n-a. Associated with every such constacyclic code C is a certain longer cyclic code C* and many properties of C can be derived by studying this cyclic code C*. This relation is not new but seems to be little known.
We propose to use this relation to investigate the minimum distance of various classes of constacyclic codes. We will study a few papers where such results are derived to see if they can also be derived in a simpler way by using this relation. Then we will try to design new good constacyclic codes with these ideas in mind.
Lõputöö kaitsmise aasta2022-2023
JuhendajaHenk D.L. Hollmann, Vitaly Skachek
Suhtlemiskeel(ed)inglise keel
Nõuded kandideerijaleThe topic is suitable both for a bachelor thesis and for a master thesis. Some background in coding theory is probably required. For a master-level thesis some knowledge of linear algebra and algebraic structures would be helpful.
Tase Bakalaureus, Magister
Märksõnad #coding theory, #finite field, minimum Hamming distance, #constacyclic
Kandideerimise kontakt
Nimi Henk D.L. Hollmann
Tel +31 619489142