Gauss periods and cyclic codes from cyclotomic sequences of small orders

2014 ◽  
Vol 31 (6) ◽  
pp. 537-546 ◽  
Author(s):  
Liqin Hu ◽  
Qin Yue ◽  
Xiaomeng Zhu
Keyword(s):  
Cyclic Codes ◽  
Gauss Periods ◽  
Cyclotomic Sequences

scholarly journals Cyclic codes from two-prime generalized cyclotomic sequences of order 6

2016 ◽  
Vol 10 (4) ◽  
pp. 707-723 ◽  
Author(s):  
Tongjiang Yan ◽  
Yanyan Liu ◽  
Yuhua Sun
Keyword(s):  
Cyclic Codes ◽  
Cyclotomic Sequences

A Large Class of p-Ary Cyclic Codes and Sequence Families

2010 ◽  
Vol E93-A (11) ◽  
pp. 2272-2277
Author(s):  
Zhengchun ZHOU ◽  
Xiaohu TANG ◽  
Udaya PARAMPALLI
Keyword(s):  
Large Class ◽  
Cyclic Codes

A Family of q-Ary Cyclic Codes with Optimal Parameters

2020 ◽  
Vol E103.A (3) ◽  
pp. 631-633
Author(s):  
Wenhua ZHANG ◽  
Shidong ZHANG ◽  
Yong WANG ◽  
Jianpeng WANG
Keyword(s):  
Cyclic Codes ◽  
Optimal Parameters

A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2237-2248 ◽  
Author(s):  
Habibul Islam ◽  
Om Prakash
Keyword(s):  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Gray Maps ◽  
Permutation Equivalent ◽  
Quasi Cyclic Codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

scholarly journals Monomial codes seen as invariant subspaces

2017 ◽  
Vol 15 (1) ◽  
pp. 1099-1107 ◽  
Author(s):  
María Isabel García-Planas ◽  
Maria Dolors Magret ◽  
Laurence Emilie Um
Keyword(s):  
Finite Field ◽  
Linear Algebra ◽  
Linear Transformation ◽  
Cyclic Codes ◽  
Invariant Subspaces ◽  
Hyperinvariant Subspaces ◽  
Computationally Expensive ◽  
The Relationship

Abstract It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field 𝔽 and hyperinvariant subspaces of 𝔽n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.

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