Abstract
We study ( 1 + λ p ) -constacyclic codes over Z p m of an arbitrary length, where λ is a unit of Z p m and m ⩾ 2 is a positive integer. We first derive the structure of ( 1 + λ p ) -constacyclic codes of length p s over GR ( p m , a ) and determine the Hamming and homogeneous distances of such constacyclic codes. These codes are then used to classify all ( 1 + λ p ) -constacyclic codes over Z p m of length N = p s n ( n prime to p). In particular, the Gray images of ( 1 + λ p ) -constacyclic codes over Z p 2 are also discussed.
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