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Modular strongly regular graphs have been introduced by Greaves et al. (Linear Algebra Appl 639:50–80, 2022). We show that a related class of isodual codes is asymptotically good. Equiangular tight frames over finite fields also introduced by the same authors in 2022 are shown here to connect with self-dual codes. We give several examples of equiangular tight frames over finite fields arising from self-dual codes. [ABSTRACT FROM AUTHOR]

In this paper, few weights linear codes over the local ring R=Fp+uFp+vFp+uvFp, with u2=v2=0,uv=vu, are constructed by using the trace function defined on an extension ring of degree m of R. These trace codes have the algebraic structure of abelian codes. Their weight distributions are evaluated explicitly by means of Gauss sums over finite fields. Two different defining sets are explored. Using a linear Gray map from R to Fp4, we obtain several families of p-ary codes from trace codes of dimension 4m. For two different defining sets: when m is even, or m is odd and p≡3(mod4). Thus we obtain two family of p-ary abelian two-weight codes, which are directly related to MacDonald codes. When m is even and under some special conditions, we obtain two classes of three-weight codes. In addition, we give the minimum distance of the dual code. Finally, applications of the p-ary image codes in secret sharing schemes are presented. [ABSTRACT FROM AUTHOR]