• Corpus ID: 201074595

RT distance and weight distributions of Type 1 constacyclic codes of length 4 p

@inproceedings{Dinh2019RTDA,
  title={RT distance and weight distributions of Type 1 constacyclic codes of length 4 p},
  author={Hai Quang Dinh and Bac Trong Nguyen and Songsak Sriboonchitta},
  year={2019}
}

• H. Dinh, B. T. Nguyen, S. Sriboonchitta
• Published 2019
• Computer Science, Mathematics

For any odd prime p such that p ≡ 1 (mod 4) , the class of Λ -constacyclic codes of length 4p over the finite commutative chain ring Ra = Fpm [u] ⟨ua⟩ = Fpm + uFpm + · · · + u Fpm , for all units Λ of Ra that have the form Λ = Λ0+uΛ1+ · · ·+uΛa−1 , where Λ0,Λ1, . . . ,Λa−1 ∈ Fpm , Λ0 ̸=0, Λ1 ̸=0 , is investigated. If the unit Λ is a square, each Λ -constacyclic code of length 4p is expressed as a direct sum of a −λ -constacyclic code and a λ -constacyclic code of length 2p . In the main case that the unit Λ is not a square, we show that any nonzero polynomial of degree < 4 over Fpm is invertible in the ambient ring Ra[x] ⟨x4p−Λ⟩ and use it to prove that the ambient ring Ra[x] ⟨x4p−Λ⟩ is a chain ring with maximal ideal ⟨x − λ0⟩ , where λ s 0 = Λ0. As an application, the number of codewords and the dual of each λ -constacyclic code are provided. Furthermore, we get the Rosenbloom–Tsfasman (RT) distance and weight distributions of such codes. Using these results, the unique MDS code with respect to the RT distance is identified.