A Class of Constacyclic Codes over <i>R</i> + <i>vR</i> and Its Gray Image

Abstract

We study (1 + 2<i>v</i>)-constacyclic codes over<i>R</i> + <i>vR</i> and their Gray images, where <i>v</i><sup>2</sup> + <i>v</i> = 0 and R is a finite chain ring with maximal ideal <<i>λ</i>> and nilpotency index <i>e.</i> It is proved that the Gray map images of a (1 + 2<i>v</i>)-constacyclic codes of length <i>n</i> over <i>R</i> + <i>vR</i> are distance-invariant linear cyclic codes of length 2<i>n</i> over <i>R</i>. The generator polynomials of this kind of codes for length <i>n</i> are determined, where n is relatively prime to <i>p</i>, <i>p</i> is the character of the field <i>R</i>/<<i>λ</i>> . Their dual codes are also discussed

Constacyclic Codes over Finite Principal Ideal Rings

“…where C 1 and C 2 are codes of length n over R since the idenpotent v and 1 − v satisfies 1 + 1 − v = 1 then by Proposition3 These codes have also been studied by [28].…”