Constant Composition Codes as Subcodes of Linear Codes

نویسندگان

  • Long Yu
  • Xiusheng Liu
چکیده

Let p be an odd prime and q be a power of p. A linear [n, k, d] code over the finite field Fq is a k-dimensional subspace of F n q with minimum Hamming distance d. Let Ai denote the number of codewords with Hamming weight i in a linear code C of length n. The weight enumerator of C is defined by 1 + A1X + A2X 2 + · · ·+ AnX. The sequence (1, A1, · · · , An) is called the weight distribution of the code C.

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

Constant composition codes derived from linear codes

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.

متن کامل

Optimal linear codes, constant-weight codes and constant-composition codes over $\Bbb F_{q}$

Optimal linear codes and constant-weight codes play very important roles in coding theory and have attached a lot of attention. In this paper, we mainly present some optimal linear codes and some optimal constant-weight codes derived from the linear codes. Firstly, we give a construction of linear codes from trace and norm functions. In some cases, its weight distribution is completely determin...

متن کامل

A Linear Algebraic Approach to Subfield Subcodes of GRS Codes

The problem of finding subfield subcodes of generalized Reed–Solomon (GRS) codes (i.e., alternant codes) is considered. A pure linear algebraic approach is taken in order to derive message constraints that generalize the well known conjugacy constraints for cyclic GRS codes and their Bose– Chaudhuri–Hocquenghem (BCH) subfield subcodes. It is shown that the presented technique can be used for fi...

متن کامل

A class of linear codes with good parameters from algebraic curves

A class of linear codes with good parameters is constructed in this correspondence. It turns out that linear codes of this class are subcodes of the subfield subcodes of Goppa’s geometry codes. In particular, we find 61 improvements on Brouwer’s table [1] based on our codes.

متن کامل

Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

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:
  • CoRR

دوره abs/1706.06997  شماره 

صفحات  -

تاریخ انتشار 2017