Naslov
Type IV-II codes over Z4 constructed from generalized bent functions

Autori
Ban, Sara ; Rukavina, Sanja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Graphs and Groups, Geometries and GAP (G2G2) Summer School - External Satellite Conference of 8ECM, Report of Contributions / - , 2021, 13-13

Skup
Graphs and Groups, Geometries and GAP (G2G2) Summer School - External Satellite Conference of 8ECM

Mjesto i datum
Rogla, Slovenija, 28.06.2021. - 02.07.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
generalized bent function, Z4-code, self-dual code, 1-design

Sažetak
A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. The subject of this talk is a construction of Type IV-II codes over Z4 from generalized bent functions. We use generalized bent functions for a construction of self-orthogonal codes over Z4 of length 2^m, for m odd, m ≥ 3, and prove that for m ≥ 5 those codes can be extended to Type IV-II Z4- codes. From that family of Type IV-II Z4-codes, we construct a family of self-dual Type II binary codes by using the Gray map. We also consider the weight distributions of the obtained codes and the structure of the supports of the minimum weight codewords, which we use for a construction of 1-designs. Some of the constructed 1-designs are affine resolvable 1-designs. For the constructed 1-designs, we examine the properties of the corresponding block intersection graphs and obtain strongly regular graphs in two cases.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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