1 research outputs found
Two-weight codes over the integers modulo a prime power
Let be a prime number. Irreducible cyclic codes of length and
dimension over the integers modulo are shown to have exactly two
nonzero Hamming weights. The construction uses the Galois ring of
characteristic and order 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 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 , is provided by
considering the Hensel lifting of these cyclic codes over the -adic numbers