Two-weight codes over the integers modulo a prime power

11/15/2019

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by   Minjia Shi, et al.

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Let p be a prime number. Irreducible cyclic codes of length p^2-1 and dimension 2 over the integers modulo p^h are shown to have exactly two nonzero Hamming weights. The construction uses the Galois ring of characteristic p^h and order p^2h. When the check polynomial is primitive, the code meets the Griesmer bound of (Shiromoto, Storme) (2012). By puncturing some projective codes are constructed. Those in length p+1 meet a Singleton-like bound of (Shiromoto , 2000). An infinite family of strongly regular graphs is constructed as coset graphs of the duals of these projective codes. A common cover of all these graphs, for fixed p, is provided by considering the Hensel lifting of these cyclic codes over the p-adic numbers.