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Advances in Mathematics of Communications (AMC)
 

The weight distributions of some irreducible cyclic codes of length $p^n$ and $2p^n$

Pages: 277 - 289, Volume 9, Issue 3, August 2015      doi:10.3934/amc.2015.9.277

 
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Pankaj Kumar - Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Pin-125001, India (email)
Monika Sangwan - Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Pin-125001, India (email)
Suresh Kumar Arora - Department of Mathematics, M. D. University, Rohtak, Pin-124001, India (email)

Abstract: In this paper, an algorithm is given for computing the weight distributions of all irreducible cyclic codes of dimension $p^jd$ generated by $x^{p^j}-1$, where $p$ is an odd prime, $j\geq 0 $ and $d > 1$. Then the weight distributions of all irreducible cyclic codes of length $p^n$ and $ 2p^n $ over $F_q$, where $n$ is a positive integer, $p$, $q$ are distinct odd primes and $q$ is primitive root modulo $ p^n$, are obtained. The weight distributions of all the irreducible cyclic codes of length $3^{n+1}$ over $F_5$ are also determined explicitly.

Keywords:  Irreducible cyclic codes, weight distribution.
Mathematics Subject Classification:  Primary: 20C05, 94B05, 94B65.

Received: October 2013;      Available Online: July 2015.

 References