At most three-weight binary linear codes from generalized Moisio’s exponential sums

2018 ◽  
Vol 87 (8) ◽  
pp. 1927-1943 ◽  
Author(s):  
Yansheng Wu ◽  
Qin Yue ◽  
Xueying Shi
Keyword(s):  
Exponential Sums ◽  
Linear Codes ◽  
Binary Linear Codes

scholarly journals Infinite families of recursive formulas generating power moments of Kloosterman sums: O −(2n,2r) case

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Dae Kim
Keyword(s):  
Exponential Sums ◽  
Linear Codes ◽  
Kloosterman Sums ◽  
Orthogonal Groups ◽  
Power Moment ◽  
Binary Linear Codes ◽  
Maximal Parabolic Subgroup ◽  
Double Cosets ◽  
Recursive Formulas ◽  
Power Moments

AbstractIn this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the special orthogonal group SO −(2n, 2r). And we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of “Gauss sums” for the orthogonal groups O −(2n, 2r).

scholarly journals Simple Tight Performance Bound Based on the GFBT for Binary Linear Codes

2020 ◽  
Vol 428 ◽  
pp. 012028
Author(s):  
Jia Liu ◽  
Mingyu Zhang ◽  
Rongjun Chen ◽  
Chaoyong Wang ◽  
Xiaofeng An ◽  
...  
Keyword(s):  
Linear Codes ◽  
Performance Bound ◽  
Binary Linear Codes

New binary linear codes which are dual transforms of good codes

1999 ◽  
Vol 45 (6) ◽  
pp. 2136-2137 ◽  
Author(s):  
D.B. Jaffe ◽  
J. Simonis
Keyword(s):  
Linear Codes ◽  
Binary Linear Codes

The ideal entropy of BCI-algebras and its application in the binary linear codes

2018 ◽  
Vol 23 (1) ◽  
pp. 39-57
Author(s):  
Mohammad Ebrahimi ◽  
Alireza Izadara
Keyword(s):  
Linear Codes ◽  
Binary Linear Codes ◽  
The Ideal
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