Cyclic Codes of Prime Power Length from Generalized Cyclotomic Classes of Order 4 and 8

2018 ◽  
Vol 53 (2) ◽  
pp. 166-171 ◽  
Author(s):  
Pan kaj ◽  
◽  
Manju Pruthi
Keyword(s):  
Prime Power ◽  
Cyclic Codes ◽  
Generalized Cyclotomic Classes

Generalized cyclotomic numbers and cyclic codes of prime power length over Z4

2019 ◽  
Vol 12 (05) ◽  
pp. 1950085 ◽  
Author(s):  
Sudhir Batra ◽  
Sonal Jain
Keyword(s):  
Prime Power ◽  
Cyclic Codes ◽  
Self Duality ◽  
Primitive Idempotents ◽  
Multiplicative Order ◽  
Cyclotomic Numbers ◽  
Explicit Expressions

Generalized cyclotomic numbers of order [Formula: see text] with respect to an odd prime power are obtained. Hence, explicit expressions for primitive idempotents in the ring [Formula: see text] are obtained in two cases, when the multiplicative order of 2 modulo [Formula: see text] is [Formula: see text] and [Formula: see text], where [Formula: see text] is an odd prime. Orthogonality and self-duality of some [Formula: see text] cyclic codes are also discussed. Further, a method for obtaining cyclic self-dual/isodual codes of length [Formula: see text] over [Formula: see text] is given.

A note on weight distributions of irreducible cyclic codes

2014 ◽  
Vol 06 (03) ◽  
pp. 1450041
Author(s):  
Anuradha Sharma ◽  
Amit K. Sharma
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Cyclic Codes ◽  
Error Performance ◽  
Space Communications ◽  
Irreducible Cyclic Codes ◽  
Weight Distributions ◽  
Long Time ◽  
Interesting Object ◽  
Object Of Study

Irreducible cyclic codes form an important family of cyclic codes and have applications in space communications. Their weight distributions measure their error performance relative to several channels, and hence have been an interesting object of study for a long time. In this note, we provide a method to determine the weight distributions of q-ary irreducible cyclic codes of length n, where q is a prime power and n is a positive integer coprime to q. This method is more effective for irreducible cyclic codes of some special lengths. We also list some optimal irreducible cyclic codes, which attain the distance bounds given in Grassl's Table [Code Tables: Bounds on the parameters of various types of codes, http://www.codetables.de ].

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
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