- Publication venue
- Publication date
- 08/11/2019
- Field of study
For prime p, GR(pa,m) represents the Galois ring of order pam and
characterise p, where a is any positive integer. In this article, we study
the Type (1) λ-constacyclic codes of length 4ps over the ring
GR(pa,m), where λ=ξ0​+pξ1​+p2z, ξ0​,ξ1​∈T(p,m) are
nonzero elements and z∈GR(pa,m). In first case, when λ is a
square, we show that any ideal of
Rp​(a,m,λ)=⟨x4ps−λ⟩GR(pa,m)[x]​ is the direct sum of the ideals of
⟨x2ps−δ⟩GR(pa,m)[x]​ and
⟨x2ps+δ⟩GR(pa,m)[x]​. In second, when
λ is not a square, we show that Rp​(a,m,λ) is a chain
ring whose ideals are ⟨(x4−α)i⟩⊆Rp​(a,m,λ), for 0≤i≤aps where αps=ξ0​.
Also, we prove the dual of the above code is ⟨(x4−α−1)aps−i⟩⊆Rp​(a,m,λ−1) and
present the necessary and sufficient condition for these codes to be
self-orthogonal and self-dual, respectively. Moreover, the Rosenbloom-Tsfasman
(RT) distance, Hamming distance and weight distribution of Type (1)
λ-constacyclic codes of length 4ps are obtained when λ is
not a square.Comment: This article has 18 pages and ready to submit in a journa