A family of linear codes with three weights

نویسندگان

  • Yang Yan
  • Fei Li
  • Qiuyan Wang
چکیده

Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three weights.

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

Intersection sets, three-character multisets and associated codes

In this article we construct new minimal intersection sets in AG(r, q2) sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in PG(r, q2) with r even and we also compute their weight distribution.

متن کامل

Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$

We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the chain ring Fp+uFp. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. Then by using a linear Gray map, we obtain an infinite family of abelian codes with few weights over Fp. In particular, we obtain an infinite family of two-weight codes which me...

متن کامل

Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3

Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...

متن کامل

Linear Codes With Two or Three Weights From Some Functions With Low Walsh Spectrum in Odd Characteristic

Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights are obtained from some functions with low Walsh spectrum in odd characteristic. Numerical results show that some of the linear codes obtained are optimal or al...

متن کامل

A new class of three-weight linear codes from weakly regular plateaued functions

Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do this, we generalize the recent contribution of Mesnager given in [Cryptography and Communications 9(1), 71-84, 2017]. We first present a new class of binary l...

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/1608.05664  شماره 

صفحات  -

تاریخ انتشار 2016