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Ring geometries, two-weight codes, and strongly regular graphs

机译：环形几何体，两个权重代码和强规则图形

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摘要

It is known that a projective linear two-weight code C over a finite field F_q corresponds both to a set of points in a projective space over F_q that meets every hyperplane in either a or b points for some integers a < b, and to a strongly regular graph whose vertices may be identified with the codewords of C. Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homogeneous weights and sets of points in an associated projective ring geometry. We will introduce regular projective two-weight codes over finite Frobenius rings, we will show that such a code gives rise to a strongly regular graph, and we will give some constructions of two-weight codes using ring geometries. All these examples yield infinite families of strongly regular graphs with non-trivial parameters.
机译：众所周知，有限域F_q上的射影线性二重码C对应于F_q上射影空间中的一些点集合，这些点与a或b点中的每个超平面相交，且某些整数a

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