RT distance and weight distributions of Type 1 constacyclic codes of  length\\ 4ps4ps4p^s over Fpm[u]⟨ua⟩Fpm[u]⟨ua⟩\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}

Hai DINH; Bac NGUYEN; Songsak SRIBOONCHITTA

Makale detayları

RT distance and weight distributions of Type 1 constacyclic codes of length\\ 4ps4ps4p^s over Fpm[u]⟨ua⟩Fpm[u]⟨ua⟩\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}

Yazarlar:

Hai DINH | Bac NGUYEN | Songsak SRIBOONCHITTA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.561-578

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745634

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

For any odd prime ppp such that pm≡1(mod4)pm≡1(mod4)p^m \equiv 1 \pmod{4}, the class of ΛΛ\Lambda-constacyclic codes of length 4ps4ps4p^s over the finite  commutative chain ring Ra=Fpm[u]⟨ua⟩=Fpm+uFpm+⋯+ua−1FpmRa=Fpm[u]⟨ua⟩=Fpm+uFpm+⋯+ua−1Fpm{\cal R}_a=\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}=\mathbb F_{p^m} + u \mathbb F_{p^m}+ \dots + u^{a-1}\mathbb F_{p^m}, for all units ΛΛ\Lambda of RaRa\mathcal R_a that have the form  Λ=Λ0+uΛ1+⋯+ua−1Λa−1Λ=Λ0+uΛ1+⋯+ua−1Λa−1\Lambda=\Lambda_0+u\Lambda_1+\dots+u^{a-1}\Lambda_{a-1}, where Λ0,Λ1,…,Λa−1∈FpmΛ0,Λ1,…,Λa−1∈Fpm\Lambda_0, \Lambda_1, \dots, \Lambda_{a-1} \in \mathbb F_{p^m}, Λ0≠0,Λ1≠0Λ0≠0,Λ1≠0\Lambda_0 \,{\not=}\, 0, \, \Lambda_1 \,{\not=}\, 0, is investigated. If the unit ΛΛ\Lambda is a square, each ΛΛ\Lambda-constacyclic code of length 4ps4ps4p^s is expressed as a direct sum of a −λ−λ-\lambda-constacyclic code and a λλ\lambda-constacyclic code of length 2ps2ps2p^s. In the main case that the unit ΛΛ\Lambda is not a square, we show that any nonzero polynomial of degree $.

Makale detayları

RT distance and weight distributions of Type 1 constacyclic codes of length\\ 4ps4ps4p^s over Fpm[u]⟨ua⟩Fpm[u]⟨ua⟩\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}

Yazarlar: Hai DINH | Bac NGUYEN | Songsak SRIBOONCHITTA

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.561-578

Belge Tipi: Makale

Yayın Tarihi: 3/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745634

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Hai DINH | Bac NGUYEN | Songsak SRIBOONCHITTA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.561-578

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745634

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098