Generalized cyclotomic numbers and cyclic codes of prime power length over Z4

2019 ◽  
Vol 12 (05) ◽  
pp. 1950085 ◽  
Author(s):  
Sudhir Batra ◽  
Sonal Jain
Keyword(s):  
Prime Power ◽  
Cyclic Codes ◽  
Self Duality ◽  
Primitive Idempotents ◽  
Multiplicative Order ◽  
Cyclotomic Numbers ◽  
Explicit Expressions

Generalized cyclotomic numbers of order [Formula: see text] with respect to an odd prime power are obtained. Hence, explicit expressions for primitive idempotents in the ring [Formula: see text] are obtained in two cases, when the multiplicative order of 2 modulo [Formula: see text] is [Formula: see text] and [Formula: see text], where [Formula: see text] is an odd prime. Orthogonality and self-duality of some [Formula: see text] cyclic codes are also discussed. Further, a method for obtaining cyclic self-dual/isodual codes of length [Formula: see text] over [Formula: see text] is given.

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.

scholarly journals On Reversibility and Self-Duality for Some Classes of Quasi-Cyclic Codes

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 143285-143293
Author(s):  
Ramy Taki Eldin ◽  
Hajime Matsui
Keyword(s):  
Cyclic Codes ◽  
Self Duality ◽  
Quasi 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.

Some special cyclic codes of length 2n

2017 ◽  
Vol 16 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Manjit Singh ◽  
Sudhir Batra
Keyword(s):  
Finite Fields ◽  
Cyclic Codes ◽  
Lucas Sequences ◽  
Explicit Expressions

The explicit expressions of generator polynomials of cyclic codes of length [Formula: see text] over finite fields are obtained. The coefficients of these generator polynomials and check polynomials are obtained through modular Lucas sequences. Further, using these polynomials, self-dual, reversible and self-orthogonal cyclic codes of length [Formula: see text] are classified.

scholarly journals Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(xpn−1)

2004 ◽  
Vol 10 (4) ◽  
pp. 653-673 ◽  
Author(s):  
Anuradha Sharma ◽  
Gurmeet K. Bakshi ◽  
V.C. Dumir ◽  
Madhu Raka
Keyword(s):  
Primitive Idempotents ◽  
Cyclotomic Numbers
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