The weight distribution of some irreducible cyclic codes

2021 ◽  
pp. 2150092
Author(s):  
Yang Liu ◽  
Yang Zhang ◽  
Zisen Kong
Keyword(s):  
Weight Distribution ◽  
Cyclic Codes ◽  
Dimension Formula ◽  
Irreducible Cyclic Codes ◽  
Special Cases

In this paper, the weight distribution of the irreducible cyclic codes over [Formula: see text] with length [Formula: see text] and dimension [Formula: see text] is settled for a few special cases. These irreducible cyclic codes have two weights or three weights or four weights.

The weight distribution of some irreducible cyclic codes

2011 ◽  
Vol 41 (10) ◽  
pp. 877-884
Author(s):  
LiWei ZENG ◽  
Yang LIU ◽  
ChangLi MA
Keyword(s):  
Weight Distribution ◽  
Cyclic Codes ◽  
Irreducible Cyclic Codes

scholarly journals The weight distribution of irreducible cyclic codes with block lengths n1((q1−1)N)

1977 ◽  
Vol 18 (2) ◽  
pp. 179-211 ◽  
Author(s):  
Tor Helleseth ◽  
Torleiv KlØve ◽  
Johannes Mykkeltveit
Keyword(s):  
Weight Distribution ◽  
Cyclic Codes ◽  
Irreducible Cyclic Codes

scholarly journals The weight distribution of some irreducible cyclic codes

2012 ◽  
Vol 18 (1) ◽  
pp. 144-159 ◽  
Author(s):  
Anuradha Sharma ◽  
Gurmeet K. Bakshi
Keyword(s):  
Weight Distribution ◽  
Cyclic Codes ◽  
Irreducible Cyclic Codes

The weight distributions of irreducible cyclic codes of length 2npm

2018 ◽  
Vol 11 (06) ◽  
pp. 1850085
Author(s):  
Monika Sangwan ◽  
Pankaj Kumar
Keyword(s):  
Finite Field ◽  
Explicit Formula ◽  
Weight Distribution ◽  
Cyclic Codes ◽  
Primitive Root ◽  
Irreducible Cyclic Codes ◽  
Weight Distributions ◽  
Primitive Root Modulo ◽  
Explicit Expressions

Let [Formula: see text] be a primitive root modulo [Formula: see text], where [Formula: see text] and [Formula: see text] are distinct odd primes. Let [Formula: see text] be a finite field. For such pair of [Formula: see text] and [Formula: see text], the explicit expressions of minimal and generating polynomials over [Formula: see text] are obtained for all irreducible cyclic codes of length [Formula: see text]. In Sec. 4, it is observed that the weight distributions of all irreducible cyclic codes of length [Formula: see text] over [Formula: see text] can be computed easily with the help of the results obtained in [P. Kumar, M. Sangwan and S. K. Arora, The weight distribution of some irreducible cyclic codes of length [Formula: see text] and [Formula: see text], Adv. Math. Commun. 9 (2015) 277–289]. An explicit formula is also given to compute the weight distributions of irreducible cyclic codes of length [Formula: see text] over [Formula: see text].

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

2014 ◽  
Vol 28 (06) ◽  
pp. 1450017 ◽  
Author(s):  
RUIHU LI ◽  
GEN XU ◽  
LUOBIN GUO
Keyword(s):  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Quantum Code ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Quantum Error ◽  
Better Than

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2 asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2 exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δ max +1 from binary primitive cyclic codes of length n = 2m-1, where δ max = 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

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