scholarly journals Multidimensional cyclic codes and Artin–Schreier type hypersurfaces over finite fields

2008 ◽  
Vol 14 (1) ◽  
pp. 44-58 ◽  
Author(s):  
Cem Güneri ◽  
Ferruh Özbudak
Keyword(s):  
Finite Fields ◽  
Cyclic Codes

On some bounds on the minimum distance of cyclic codes over finite fields

2014 ◽  
Vol 76 (2) ◽  
pp. 173-178
Author(s):  
Ferruh Özbudak ◽  
Seher Tutdere ◽  
Oğuz Yayla
Keyword(s):  
Finite Fields ◽  
Minimum Distance ◽  
Cyclic Codes

A class of minimal cyclic codes over finite fields

2013 ◽  
Vol 74 (2) ◽  
pp. 285-300 ◽  
Author(s):  
Bocong Chen ◽  
Hongwei Liu ◽  
Guanghui Zhang
Keyword(s):  
Finite Fields ◽  
Cyclic Codes

scholarly journals LCD Cyclic Codes Over Finite Fields

2017 ◽  
Vol 63 (7) ◽  
pp. 4344-4356 ◽  
Author(s):  
Chengju Li ◽  
Cunsheng Ding ◽  
Shuxing Li
Keyword(s):  
Finite Fields ◽  
Cyclic Codes

scholarly journals Enumeration of self-dual cyclic codes of some specific lengths over finite fields

2018 ◽  
Vol 10 (03) ◽  
pp. 1850031 ◽  
Author(s):  
Supawadee Prugsapitak ◽  
Somphong Jitman
Keyword(s):  
Characteristic Function ◽  
Finite Field ◽  
Finite Fields ◽  
Linear Codes ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Efficient Algorithms ◽  
Important Class ◽  
Field Characteristic ◽  
Positive Integers

Self-dual cyclic codes form an important class of linear codes. It has been shown that there exists a self-dual cyclic code of length [Formula: see text] over a finite field if and only if [Formula: see text] and the field characteristic are even. The enumeration of such codes has been given under both the Euclidean and Hermitian products. However, in each case, the formula for self-dual cyclic codes of length [Formula: see text] over a finite field contains a characteristic function which is not easily computed. In this paper, we focus on more efficient ways to enumerate self-dual cyclic codes of lengths [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are positive integers. Some number theoretical tools are established. Based on these results, alternative formulas and efficient algorithms to determine the number of self-dual cyclic codes of such lengths are provided.

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