Optimal linear codes, constant-weight codes and constant-composition codes over $\Bbb F_{q}$
نویسندگان
چکیده
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 determined. In particular, we obtain two classes of optimal linear codes achieving the Griesmer bound and the Plotkin bound. Secondly, we give two classes of q-ary optimal constant-weight codes, which are subcodes of the linear codes, achieving the generalized Johnson bound I. Finally, we give a family of optimal constant-composition codes, which are subcodes of the linear codes, achieving the well-known Luo-Fu-Vinck-Chen bound. Index Terms linear codes, constant-weight codes, constant-composition codes, Gauss sums,
منابع مشابه
Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes
An optimal constant-composition or constant-weight code of weight has linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper ...
متن کاملOn Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over $R$. Further, we give bounds on the minimum distance of LCD codes over $\F_q$ and extend these to codes ove...
متن کاملOptimal 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 کاملConstant 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 کاملOn constant-composition codes over Zq
A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the -ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes the Graham–Sloane bound for binary constant-wei...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1605.04063 شماره
صفحات -
تاریخ انتشار 2016