Seminar za konačne geometrije i grupe

26.04.2018 - 12:15 - 13:30
U četvrtak, 26.4.2018. s početkom u 12:15 sati održat će se seminar:
Marcus Greferath:
Spectral Techniques in Codes over Rings, and Best's (10,40,4) Code
Pozivaju se članovi seminara i ostali zainteresirani.
Seminar se održava u predavaonici D-102 na FER-u.
Kristijan Tabak
Abstract: A non-linear cyclic binary code of length 10 and minimum distance 4  that
contains 40 codewords was found by M.~Best at the end of the seventies. It was
shown to be unique by Litsyn and Vardy in 1993 and resisted every attempt to be
linearized by changing the alphabet structure to a ring like {\mathbb Z}_4. Conway
and Sloane discovered however in 1994 that it is most convenient to rewrite this code
as what is called the (cyclic) non-linear (5,40,4) pentacode over {\mathbb Z}_4.
This talk briefly revisits spectral techniques on finite Frobenius rings and attempts to provide
a mathematical preparation to represent this pentacode as a group co-set.
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