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].

scholarly journals Primitive Idempotents of Irreducible Cyclic Codes of Length n

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yuqian Lin ◽  
Qin Yue ◽  
Yansheng Wu
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Matrix Method ◽  
Cyclic Codes ◽  
Prime Divisors ◽  
Primitive Idempotents ◽  
Irreducible Cyclic Codes

Let Fq be a finite field with q elements and n a positive integer. In this paper, we use matrix method to give all primitive idempotents of irreducible cyclic codes of length n, whose prime divisors divide q-1.

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 Infinite Families of 2-Designs from a Class of Linear Codes Related to Dembowski-Ostrom Functions

2021 ◽  
pp. 1-15
Author(s):  
Rong Wang ◽  
Xiaoni Du ◽  
Cuiling Fan ◽  
Zhihua Niu
Keyword(s):  
Finite Field ◽  
Weight Distribution ◽  
Coding Theory ◽  
Exponential Sums ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Research Interest ◽  
Combinatorial Formula ◽  
Text Design ◽  
Fixed Weight

Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial [Formula: see text]-designs have attracted lots of research interest for decades. The interplay between coding theory and [Formula: see text]-designs started many years ago. It is generally known that [Formula: see text]-designs can be used to derive linear codes over any finite field, and that the supports of all codewords with a fixed weight in a code also may hold a [Formula: see text]-design. In this paper, we first construct a class of linear codes from cyclic codes related to Dembowski-Ostrom functions. By using exponential sums, we then determine the weight distribution of the linear codes. Finally, we obtain infinite families of [Formula: see text]-designs from the supports of all codewords with a fixed weight in these codes. Furthermore, the parameters of [Formula: see text]-designs are calculated explicitly.

GRÖBNER BASIS TECHNIQUES TO COMPUTE WEIGHT DISTRIBUTIONS OF SHORTENED CYCLIC CODES

2007 ◽  
Vol 06 (03) ◽  
pp. 403-414 ◽  
Author(s):  
MASSIMILIANO SALA
Keyword(s):  
Weight Distribution ◽  
Gröbner Basis ◽  
Cyclic Codes ◽  
Grobner Basis ◽  
Weight Distributions

Using Gröbner techniques, we can exhibit a method to get the distance and weight distribution of cyclic codes and shortened cyclic codes, improving earlier similar results for the distance of 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 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.

scholarly journals The weight distributions of irreducible cyclic codes of length 2m

2007 ◽  
Vol 13 (4) ◽  
pp. 1086-1095 ◽  
Author(s):  
Anuradha Sharma ◽  
Gurmeet K. Bakshi ◽  
Madhu Raka
Keyword(s):  
Cyclic Codes ◽  
Irreducible Cyclic Codes ◽  
Weight Distributions
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