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Further Results on Homogeneous Two-Weight Codes
The results of [1,2] on linear homogeneous two-weight codes over finite
Frobenius rings are exended in two ways: It is shown that certain
non-projective two-weight codes give rise to strongly regular graphs in the way
described in [1,2]. Secondly, these codes are used to define a dual two-weight
code and strongly regular graph similar to the classical case of projective
linear two-weight codes over finite fields [3].Comment: 7 pages, reprinted from the conference proceedings of the Fifth
International Workshop on Optimal Codes and Related Topics (OC2007
On the Weight Distribution of Codes over Finite Rings
Let R > S be finite Frobenius rings for which there exists a trace map T from
R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is
an S-linear subring-subcode of a left linear code over R. We consider functions
f for which the homogeneous weight distribution of C can be computed. In
particular, we give constructions of codes over integer modular rings and
commutative local Frobenius that have small spectra.Comment: 18 p
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