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View the PDF document Some error correcting codes related to finite groups
Author:Tekabu, Tokaua.
Institution: University of the South Pacific.
Award: M.Sc.
Date: 2008.
Call No.: pac In Process
BRN: 1176922
Copyright:Under 10% of this thesis may be copied without the authors written permission

Abstract: Error correcting codes related to nite groups are codes associated with the null space of an incidence matrix Vk(L(G)) of lattices of subgroups of some nite groups G. We call such codes Combinatorial codes. The nite groups we are considering are of the following form: Cyclic groups Zn where n is any square-free integer, that is any integer of the form p1p2 : : : pn , where p1; p2; : : : ; pn are dierent primes. Cyclic groups Zn where n = st , where s is any square free primes and t > 1 is integer. Some non-cyclic Abelian groups in the form G = Zp Zp | {z } n , where p is prime. We investigate properties of such codes, namely lengths, dimensions, ranks, weight distributions and minimum distances over nite elds GF(p) , where p = 2; 3 and 5 . We obtain such properties by constructing the weight enumerator of the codes, using the assistance of GAP and GUAVA computer packages. We extend Lefmann's theorem, as well as Mnukhin and Siemons ndings on the minimum distance of codes related to Boolean lattices for small characteristics, 0 < p < n . We also present tables of ranks over GF(p) of the mysterious matrices in Hamanda's formula (incidence matrices of lattices of n -dimensional subspace over GF(q) ) for some cases when p = q . iv
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