Classification of Griesmer codes and dual transform
نویسنده
چکیده
In this work, we consider a classification of infinite families of linear codes which achieve the Griesmer bound, using the projective dual transform. We investigate the correspondence between families of linear codes with given properties via dual transform.
منابع مشابه
New few weight codes from trace codes over a local Ring
In this paper, new few weights linear codes over the local ring R = Fp+uFp+vFp+uvFp, with u2 = v2 = 0, uv = vu, are constructed by using the trace function defined over an extension ring of degree m. These trace codes have the algebraic structure of abelian codes. Their weight distributions are evaluated explicitly by means of Gaussian sums over finite fields. Two different defining sets are ex...
متن کاملTwo-weight and three-weight codes from trace codes over
We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring Fp+uFp+ vFp+uvFp, where u 2 = 0, v = 0, uv = vu. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. With a linear Gray map, we obtain a class of abelian three-weight codes and two-weight codes...
متن کاملSome New Results on Optimal Codes Over F5
We present some results on almost maximum distance separable (AMDS) codes and Griesmer codes of dimension 4 over F5. We prove that no AMDS code of length 13 and minimum distance 5 exists, and we give a classification of some AMDS codes. Moreover, we classify the projective strongly optimal Griesmer codes over F5 of dimension 4 for some values of the minimum distance.
متن کاملOn the Griesmer bound for nonlinear codes
Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family of systematic nonlinear codes for which the Griesmer bound holds. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit counterexamples. On the other hand, we ar...
متن کاملOn codes meeting the Griesmer bound
We investigate codes meeting the Griesmer bound. The main theorem of this article is the generalization of the nonexistence theorem of [7] to a larger class of codes. keywords: Griesmer bound, extending codes, nonexistence theorem, code construction
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 309 شماره
صفحات -
تاریخ انتشار 2009