ON THE POSSIBILITY OF GROUP-THEORETIC DESCRIPTION OF ANEQUIVALENCE RELATION CONNECTED TO THE PROBLEM OFCOVERING SUBSETS IN FINITE FIELDS WITH COSETS OF LINEARSUBSPACES

Author(s)

ON THE POSSIBILITY OF GROUP-THEORETIC DESCRIPTION OF ANEQUIVALENCE RELATION CONNECTED TO THE PROBLEM OFCOVERING SUBSETS IN FINITE FIELDS WITH COSETS OF LINEARSUBSPACES Davit Sargsyan

LetFnqbe ann-dimensional vector space over a finite fieldFq. LetC(Fnq)denote the set of all cosets of linear subspaces inFnq. CosetsH1,H2,...,Hsare called exclusive ifHi6⊆Hj,1≤i<j≤s. A permutationfofC(Fnq)is called aC-permutation, if for any exclusive cosetsH,H1,H2,...,HssuchthatH⊆H1∪H2∪···∪Hswe have:i)cosetsf(H),f(H1),f(H2),...,f(Hs)are exclusive;ii)cosetsf−1(H),f−1(H1),f−1(H2),...,f−1(Hs)are exclusive;iii)f(H)⊆f(H1)∪f(H2)∪···∪f(Hs);vi)f−1(H)⊆f−1(H1)∪f−1(H2)∪···∪f−1(Hs).In this paper we show that the set of allC-permutations ofC(Fnq)is theGeneral Semiaffine Group of degreenoverFq.

DOI: 10.46991/PYSU:A/2019.53.1.023 Physical and Mathematical Sciences, 53(1 (248) 23-27

Download PDF

Keywords

finite field, coset, covering, bijection, linearized disjunctivenormal form, general affine group, general semiaffine group.

Check for updates

Share

Contact admin with any questions, comments or concerns

[email protected]