Weight enumerator of some irreducible cyclic codes
نویسندگان
چکیده
In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length n over a finite field Fq, in the case which each prime divisor of n is also a divisor of q − 1.
منابع مشابه
The Complete Weight Enumerator of Several Cyclic Codes
Cyclic codes have attracted a lot of research interest for decades. In this paper, for an odd prime p, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding exponential sums. As applications of this general strategy, we determine the complete weight enumerator of several p-ary cyclic codes and give some examples t...
متن کاملOn the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and expl...
متن کاملVectorial Boolean functions and linear codes in the context of algebraic attacks
In this paper we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and certain 2n-ary cyclic codes (which we prove that they are LCD codes) extending results due to Rønjom and Helleseth. The knowledge of the minimum distance of thos...
متن کاملThe dimension and minimum distance of two classes of primitive BCH codes
Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes – a family of cyclic codes – in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the narrow-sense primitive BCH codes. However, ...
متن کاملWeight distributions of cyclic codes with respect to pairwise coprime order elements
Let Fq be a finite field with q elements, where q = p , p is a prime, and s is a positive integer. An [n, k, d] linear code C is a k-dimensional subspace of Fq with minimum distance d. It is called cyclic if (c0, c1, . . . , cn−1) ∈ C implies (cn−1, c0, c1, . . . , cn−2) ∈ C. By identifying the vector (c0, c1, . . . , cn−1) ∈ Fq with c0 + c1x+ c2x 2 + · · ·+ cn−1c ∈ Fq[x]/(x − 1), any code C of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Des. Codes Cryptography
دوره 78 شماره
صفحات -
تاریخ انتشار 2016