Cyclic codes over finite rings
نویسنده
چکیده
It is well known that cyclic linear codes of length n over a (finite) field F can be characterized in terms of the factors of the polynomial x"-1 in F[x]. This paper investigates cyclic linear codes over arbitrary (not necessarily commutative) finite tings and proves the above characterization to be true for a large class of such codes over these rings. (~) 1997 Elsevier Science B.V. All rights reserved
منابع مشابه
On Isodual Cyclic Codes over Finite Fields and Finite Chain Rings: Monomial Equivalence
This paper present the construction cyclic isodual codes over finite fields and finite chain rings. These codes are monomially equivalent to their dual. Conditions are given for the existence of cyclic isodual codes. In addition, the concept of duadic codes over finite fields is extended to finite chain rings. Several constructions of isodual cyclic codes and self-dual codes are given.
متن کاملThe Gray Image of Codes over Finite Chain Rings
The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...
متن کاملOn Skew Cyclic Codes over a Finite Ring
In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
متن کاملAdditive cyclic codes over finite commutative chain rings
Additive cyclic codes over Galois rings were investigated in [3]. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in [3], whereas the other one has some unusual propertie...
متن کاملCyclic Codes over Some Finite Rings
In this paper cyclic codes are established with respect to the Mannheim metric over some finite rings by using Gaussian integers and the decoding algorithm for these codes is given. AMS Classification: 94B05, 94B60
متن کاملCyclic Codes over Some Finite Quaternion Integer Rings
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and decoding algorithm for these codes is given. 2000 AMS Classification: 94B05, 94B15, 94B35, 94B60
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:
- Discrete Mathematics
دوره 177 شماره
صفحات -
تاریخ انتشار 1997