Cyclic and Negacyclic Codes Over Finite Chain Rings

Dinh, Hai Q.; López-Permouth, Sergio R.

doi:10.1109/tit.2004.831789

Cited by 345 publications

(275 citation statements)

References 17 publications

Supporting

Mentioning

254

Contrasting

Unclassified

Order By: Relevance

“…Dinh and López-Permouth in [28] generalized that to obtain that this fact holds true for cyclic and negacyclic codes of odd lengths over any finite chain ring. Batoul et al in [2,Proposition 3.4] extended this result to a more general setting.…”

Section: Generalization To Constacyclic Codesmentioning

confidence: 89%

Recent progress on weight distributions of cyclic codes over finite fields

Dinh¹,

Li²,

Yue³

2015

JACODESMATH

View full text Add to dashboard Cite

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions.

show abstract

Section: Generalization To Constacyclic Codesmentioning

confidence: 89%

Recent progress on weight distributions of cyclic codes over finite fields

Dinh¹,

Li²,

Yue³

2015

JACODESMATH

View full text Add to dashboard Cite

show abstract

“…Many of the works in the literature deal with the case wherein R is a finite chain ring [1][2][3][4][5][6][7][8][9][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Some results on cyclic codes over the ring $R_{2,m}$

Sobhani¹,

Molakarimi²

2013

Turk J Math

View full text Add to dashboard Cite

In this paper, cyclic codes of arbitrary length n over the ring R2,m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F2m -basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one correspondence between cyclic codes of length 2n , n odd, over the ring R k−1,m and cyclic codes of length n over the ring R k,m . By determining the complete structure of cyclic codes of length 2 over R2,m , a mass formula for the number of these codes is given. Using this and the mentioned correspondence, the number of ideals of the rings R2,m and R3,m is determined. As a corollary, the number of cyclic codes of odd length n over the rings R2,m and R3,m is obtained.

show abstract

“…In particular, cyclic and negacyclic codes over finite rings have received much attention in series of paper [4][5][6][7][8][9][10][11][12][13][14][15]. Dinh and Lopez-Permouth in [16] have considered the ring Z 2 m (m ≥ 2) and studied the negacyclic codes of length 2 t (t ≥ 1) over that. They have provided complete list of negacyclic codes of length 2 t Over Z 2m .…”

Section: Introductionmentioning

confidence: 99%