Primitive idempotents of irreducible cyclic codes and self-dual cyclic codes over Galois rings

2018 ◽  
Vol 341 (6) ◽  
pp. 1755-1767 ◽  
Author(s):  
Yansheng Wu ◽  
Qin Yue ◽  
Fengwei Li
Keyword(s):  
Cyclic Codes ◽  
Galois Rings ◽  
Primitive Idempotents ◽  
Irreducible Cyclic Codes

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.

Two-Weight Codes Punctured from Irreducible Cyclic Codes

2008 ◽  
Author(s):  
Cunsheng Ding ◽  
Jinquan Luo ◽  
Harald Niederreiter
Keyword(s):  
Cyclic Codes ◽  
Irreducible Cyclic Codes

EXPLICIT DETERMINATION OF CERTAIN MINIMAL ABELIAN CODES AND THEIR MINIMUM DISTANCES

2012 ◽  
Vol 05 (01) ◽  
pp. 1250002
Author(s):  
Pooja Grover ◽  
Ashwani K. Bhandari
Keyword(s):  
Abelian Groups ◽  
Cyclic Codes ◽  
Group Algebras ◽  
Primitive Idempotents ◽  
Abelian Codes ◽  
Complete Set ◽  
Minimum Distances ◽  
Minimal Codes ◽  
Explicit Determination

In this paper minimal codes for several classes of non-cyclic abelian groups have been constructed by explicitly determining a complete set of primitive idempotents in the corresponding group algebras. Some classes of non-p-groups have also been considered. The minimum distances of such abelian codes have been discussed and compared to the minimum distances of cyclic codes of same lengths and dimensions over the same field.

scholarly journals Enumeration and construction of additive cyclic codes over Galois rings

2015 ◽  
Vol 338 (6) ◽  
pp. 922-937 ◽  
Author(s):  
Yonglin Cao ◽  
Jian Gao ◽  
Fang-Wei Fu ◽  
Yuan Cao
Keyword(s):  
Cyclic Codes ◽  
Galois Rings

Skew quasi-cyclic codes over Galois rings

2011 ◽  
Vol 62 (1) ◽  
pp. 85-101 ◽  
Author(s):  
Maheshanand Bhaintwal
Keyword(s):  
Cyclic Codes ◽  
Galois Rings ◽  
Quasi Cyclic Codes

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
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