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Discrete Mathematics, ISSN 0012-365X, 02/2013, Volume 313, Issue 4, pp. 434 - 446
The objectives of this paper are to survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem... 
Weight distribution | Cyclotomy | Gaussian periods | Difference sets | Irreducible cyclic codes | Cyclic codes | DISTRIBUTIONS | MATHEMATICS | PERIOD POLYNOMIALS | GAUSS SUMS
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2015, Volume 61, Issue 9, pp. 4905 - 4913
Journal Article
Discrete Mathematics, ISSN 0012-365X, 06/2018, Volume 341, Issue 6, pp. 1755 - 1767
Let be the Galois ring of characteristic and cardinality . Firstly, we give all primitive idempotent generators of irreducible cyclic codes of length over ,... 
Weight distribution | Primitive idempotents | Irreducible cyclic codes | Self-dual cyclic codes | MATHEMATICS | LENGTH | ENUMERATION
Journal Article
Discrete Mathematics, ISSN 0012-365X, 09/2014, Volume 331, pp. 142 - 150
In this paper, the explicit expressions for the generating idempotents, check polynomials and the parameters of all minimal cyclic codes of length over are... 
Minimal cyclic code | Check polynomial | Cyclic code | Hamming distance | Irreducible character | Primitive idempotent | 2P(N) | MATHEMATICS | LENGTH P(N)Q | ROOT CONSTACYCLIC CODES | Integers | Mathematical analysis | Polynomials
Journal Article
Discrete Mathematics, ISSN 0012-365X, 01/2017, Volume 340, Issue 1, pp. 3197 - 3206
Let be a finite field of odd order and , where are positive integers, are distinct odd primes and . In this paper, we study the irreducible factorization of... 
Irreducible factorization | Primitive idempotent | Irreducible cyclic code | MATHEMATICS | LENGTH P(N)Q | EXPLICIT FACTORIZATION | IDEMPOTENTS
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2009, Volume 55, Issue 3, pp. 955 - 960
Irreducible cyclic codes have been an interesting subject of study for a long time. Their weight distribution is known in only a few cases. In this paper, the... 
Computer science | Linear code | Fourier transforms | linear codes | Gaussian processes | Cyclotomy | Gaussian periods | irreducible cyclic codes | Distributed computing | Linear codes | Irreducible cyclic codes | COMPUTER SCIENCE, INFORMATION SYSTEMS | PERIOD POLYNOMIALS | SUMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Information theory | Data encryption | Codes | Standards
Journal Article
Finite Fields and Their Applications, ISSN 1071-5797, 07/2015, Volume 34, pp. 208 - 234
Let be a finite field of elements with and , where is an odd prime. In this paper, we use matrix method to give all primitive idempotents in two rings and .... 
Finite field | Primitive idempotent | Irreducible cyclic code
Journal Article
by Li, FW and Yue, Q and Li, CJ
FINITE FIELDS AND THEIR APPLICATIONS, ISSN 1071-5797, 07/2015, Volume 34, pp. 208 - 234
Let F-q be a finite field of q elements with q = 3 (mod 8) and p\q - 1, where p is an odd prime. In this paper, we use matrix method to give all primitive... 
MATHEMATICS | Finite field | MATHEMATICS, APPLIED | Irreducible cyclic code | Primitive idempotent
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 4/2018, Volume 86, Issue 4, pp. 835 - 840
Journal Article
Finite Fields and Their Applications, ISSN 1071-5797, 09/2014, Volume 29, pp. 225 - 242
Let be a finite field with elements and , , , where , are distinct primes and . In this paper, we give all irreducible factors of over and all primitive... 
Finite field | Primitive idempotent | Irreducible cyclic code | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Finite Fields and Their Applications, ISSN 1071-5797, 11/2014, Volume 30, pp. 100 - 120
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In... 
Linear codes | Almost perfect nonlinear functions | Perfect nonlinear functions | Cyclic codes | Irreducible polynomials | MATHEMATICS | POWER FUNCTIONS | MATHEMATICS, APPLIED | MAPPINGS | WEIGHT DISTRIBUTION | Access control | Information storage and retrieval | Computer science | Consumer electronics
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2010, Volume 56, Issue 6, pp. 2568 - 2570
Elementary properties of the trace map are used to construct a family of two-weight, irreducible cyclic codes. These codes are neither subfield codes nor are... 
Codes | trace | irreducible | Polynomials | two-weight | Australia | Galois fields | Hamming weight | cyclic | Trace | Cyclic | Irreducible | Two-weight | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Coding theory | Research | Data encryption | Cryptography | Construction | Information theory
Journal Article
by Vega, G
IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2012, Volume 58, Issue 4, pp. 2263 - 2264
A class of two-weight non-irreducible cyclic codes was recently presented by Ma . This class of codes generalizes and extends some of the codes presented in... 
Computers | Linear code | Non-irreducible cyclic codes | weight distribution | two-weight cyclic codes | Polynomials | Cryptography | Indexes | Galois fields | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Error-correcting codes | Coding theory | Research | Codes | Information theory
Journal Article
Asian-European Journal of Mathematics, ISSN 1793-5571, 10/2017
Journal Article
Finite Fields and Their Applications, ISSN 1071-5797, 03/2018, Volume 50, pp. 319 - 337
We explicitly determine the values of reduced cyclotomic periods of order , , for finite fields of characteristic . These evaluations are applied to obtain... 
Weight distribution | Cyclotomic period | Reduced period polynomial | Irreducible cyclic code | f-nomial Gaussian period | Factorization | Period polynomial
Journal Article
by Vega, G
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, ISSN 0938-1279, 08/2018, Volume 29, Issue 4, pp. 363 - 370
We generalize and simplify the results of Sharma and Bakshi (Finite Fields Appl 18(1):144-159 2012) on the weight-distributions of irreducible cyclic codes of... 
Weight distribution | Weight enumerator polynomial | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | Irreducible cyclic codes
Journal Article
Cryptography and Communications, ISSN 1936-2447, 2019
Journal Article
Finite Fields and Their Applications, ISSN 1071-5797, 2012, Volume 18, Issue 1, pp. 144 - 159
Let be the finite field with elements, be an odd prime co-prime to and be an integer. In this paper, we explicitly determine the weight distribution of all the... 
Irreducible cyclic codes | Weight distribution | Cyclotomic cosets | MATHEMATICS | MATHEMATICS, APPLIED | GAUSS SUMS
Journal Article
FINITE FIELDS AND THEIR APPLICATIONS, ISSN 1071-5797, 03/2018, Volume 50, pp. 319 - 337
We explicitly determine the values of reduced cyclotomic periods of order 2(m), m >= 4, for finite fields of characteristic p equivalent to 3 or 5 (mod 8).... 
MATHEMATICS | Weight distribution | MATHEMATICS, APPLIED | DIAGONAL EQUATIONS | Cyclotomic period | Reduced period polynomial | Irreducible cyclic code | f-nomial Gaussian period | Factorization | Period polynomial | SUMS
Journal Article
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