GROUP CODES OVER NON-ABELIAN GROUPS
2013 ◽
Vol 12
(07)
◽
pp. 1350037
◽
Keyword(s):
Let G be a finite group and F a field. We show that all G-codes over F are abelian if the order of G is less than 24, but for F = ℤ5 and G = S4 there exist non-abelian G-codes over F, answering to an open problem posed in [J. J. Bernal, Á. del Río and J. J. Simón, An intrinsical description of group codes, Des. Codes Cryptogr.51(3) (2009) 289–300]. This problem is related to the decomposability of a group as the product of two abelian subgroups. We consider this problem in the case of p-groups, finding the minimal order for which all p-groups of such order are decomposable. Finally, we study if the fact that all G-codes are abelian remains true when the base field is changed.
1998 ◽
Vol 57
(2)
◽
pp. 181-188
◽
Keyword(s):
1996 ◽
Vol 16
(1)
◽
pp. 45-50
◽
1979 ◽
Vol 20
(1)
◽
pp. 57-70
◽
Keyword(s):
1969 ◽
Vol 21
◽
pp. 684-701
◽
Keyword(s):
1982 ◽
Vol 33
(1)
◽
pp. 76-85
Keyword(s):
Keyword(s):
Keyword(s):
2018 ◽
Vol 17
(07)
◽
pp. 1850122
◽