A note on weight distributions of irreducible cyclic codes

2014 ◽  
Vol 06 (03) ◽  
pp. 1450041
Author(s):  
Anuradha Sharma ◽  
Amit K. Sharma
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Cyclic Codes ◽  
Error Performance ◽  
Space Communications ◽  
Irreducible Cyclic Codes ◽  
Weight Distributions ◽  
Long Time ◽  
Interesting Object ◽  
Object Of Study

Irreducible cyclic codes form an important family of cyclic codes and have applications in space communications. Their weight distributions measure their error performance relative to several channels, and hence have been an interesting object of study for a long time. In this note, we provide a method to determine the weight distributions of q-ary irreducible cyclic codes of length n, where q is a prime power and n is a positive integer coprime to q. This method is more effective for irreducible cyclic codes of some special lengths. We also list some optimal irreducible cyclic codes, which attain the distance bounds given in Grassl's Table [Code Tables: Bounds on the parameters of various types of codes, http://www.codetables.de ].

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 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

scholarly journals Weight distributions of some irreducible cyclic codes

1986 ◽  
Vol 46 (173) ◽  
pp. 341-341 ◽  
Author(s):  
Robert Segal ◽  
Robert L. Ward
Keyword(s):  
Cyclic Codes ◽  
Irreducible Cyclic Codes ◽  
Weight Distributions

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 The weight distributions of some irreducible cyclic codes of length $p^n$ and $2p^n$

2015 ◽  
Vol 9 (3) ◽  
pp. 277-289 ◽  
Author(s):  
Pankaj Kumar ◽  
◽  
Monika Sangwan ◽  
Suresh Kumar Arora ◽  
Keyword(s):  
Cyclic Codes ◽  
Irreducible Cyclic Codes ◽  
Weight Distributions

Prophet Inequalities for Independent and Identically Distributed Random Variables from an Unknown Distribution

2021 ◽  
Author(s):  
José Correa ◽  
Paul Dütting ◽  
Felix Fischer ◽  
Kevin Schewior
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Optimal Solution ◽  
Random Order ◽  
Secretary Problem ◽  
Maximum Value ◽  
Optimal Stopping Theory ◽  
Long Time ◽  
Object Of Study ◽  
Independent And Identically Distributed

A central object of study in optimal stopping theory is the single-choice prophet inequality for independent and identically distributed random variables: given a sequence of random variables [Formula: see text] drawn independently from the same distribution, the goal is to choose a stopping time τ such that for the maximum value of α and for all distributions, [Formula: see text]. What makes this problem challenging is that the decision whether [Formula: see text] may only depend on the values of the random variables [Formula: see text] and on the distribution F. For a long time, the best known bound for the problem had been [Formula: see text], but recently a tight bound of [Formula: see text] was obtained. The case where F is unknown, such that the decision whether [Formula: see text] may depend only on the values of the random variables [Formula: see text], is equally well motivated but has received much less attention. A straightforward guarantee for this case of [Formula: see text] can be derived from the well-known optimal solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F, and we show that, even with o(n) samples, [Formula: see text]. On the other hand, n samples allow for a significant improvement, whereas [Formula: see text] samples are equivalent to knowledge of the distribution: specifically, with n samples, [Formula: see text] and [Formula: see text], and with [Formula: see text] samples, [Formula: see text] for any [Formula: see text].

scholarly journals Metode dan Pendekatan dalam Studi Islam: Pembacaan atas Pemikiran Charles J. Adams

2014 ◽  
Vol 2 (1) ◽  
pp. 27
Author(s):  
Luluk Fikri Zuhriyah
Keyword(s):  
Single Point ◽  
Belief System ◽  
Sociology Of Religion ◽  
Point Of View ◽  
Complex Nature ◽  
The West ◽  
History Of ◽  
Interesting Object ◽  
Object Of Study ◽  
Oriental Studies

<p>Islam has been an interesting object of study for both Muslims and non-Muslims over a long period of time. A number of methods and approaches have also been introduced. In due time, Islam is now no longer understood solely as a doctrine or a set of belief system. Nor is it interpreted merely as an historical process. Islam is a social system comprising of a complex web of human experience. Islam does not only consist of formal codes that individuals should look at and obey. It also contains some cultural, political and economic values. Islam is a civilization. Given the complex nature of Islam it is no longer possible to deal with it from a single point of view. An inter-disciplinary perspective is required.</p><p>In the West, social and humanities sciences have long been introduced in the study of religion; studies that put a stronger emphasis on what we currently know as the history of religion, psychology of religion, sociology of religion and so on. This kind of approach in turn, is also applied in the Western studies of the Eastern religions and communities.</p><p>Islam as a religion is also dealt with in this way in the West. It is treated as part of the oriental culture to the extent that—as Muhammad Abdul Raouf has correctly argued—Islamic studies became identical to the oriental studies. By all means, the West preceded the Muslims in studying Islam from modern perspectives; perspective that puts more emphasis on social, cultural, behavioral, political and economic aspects. Among the Western scholars that approach Islam from this angle is Charles Joseph Adams whose thought this research is interested to explore.</p>

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