Cyclic codes over GR(p2, m) of length pk

نویسندگان

  • Han Mao Kiah
  • Ka Hin Leung
  • San Ling
چکیده

We study cyclic codes of length pk over GR(p2,m), or equivalently, ideals of the ring GR(p2,m)/ 〈upk − 1〉. We derive a method of representing the ideals, and classify all ideals in the ring GR(p2,m)/ 〈upk − 1〉. We also analyse the duals, and identify the self-dual ideals. © 2008 Elsevier Inc. All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A note on cyclic codes over GR(p 2, m) of length p k

The number of self-dual cyclic codes of length pk over GR(p2,m) is determined by the nullity of a certain matrix M(pk, i1). With the aid of Genocchi numbers, we determine the nullity of M(pk, i1) and hence determine completely the number of such codes.

متن کامل

Hermitian Self-Dual Cyclic Codes of Length $p^a$ over $GR(p^2, s)$

In this paper, we study cyclic codes over the Galois ring GR(p, s). The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length pa over GR(p, s). Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over GR(p, s). S...

متن کامل

Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p,m) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding ...

متن کامل

Left dihedral codes over Galois rings ${\rm GR}(p^2,m)$

Let D2n = 〈x, y | x = 1, y = 1, yxy = x〉 be a dihedral group, and R = GR(p, m) be a Galois ring of characteristic p and cardinality p where p is a prime. Left ideals of the group ring R[D2n] are called left dihedral codes over R of length 2n, and abbreviated as left D2n-codes over R. Let gcd(n, p) = 1 in this paper. Then any left D2n-code over R is uniquely decomposed into a direct sum of conca...

متن کامل

On cyclic codes and quasi-cyclic codes over Zq + uZq

Let R = Zq + uZq, where q = p and u = 0. In this paper, some structural properties of cyclic codes and quasi-cyclic (QC) codes over the ring R are considered. A QC code of length ln with index l over R is viewed both as in the conventional row circulant form and also as an R[x]/(x − 1)-submodule of GR(R, l)[x]/(x − 1), where GR(R, l) is the Galois extension ring of degree l over R. A necessary ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Finite Fields and Their Applications

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2008