The nonexistence of some quaternary linear codes of dimension 5

نویسنده

  • Tatsuya Maruta
چکیده

We prove the nonexistence of linear codes with parameters [400; 5; 299]4, [401; 5; 300]4, [405; 5; 303]4, [406; 5; 304]4, [485; 5; 363]4 and [486; 5; 364]4 attaining the Griesmer bound. For that purpose we give a characterization of linear codes with parameters [86; 4; 64]4, [101; 4; 75]4, [102; 4; 76]4 and [122; 4; 91]4. c © 2001 Elsevier Science B.V. 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

On the nonexistence of linear perfect Lee codes

In 1968, Golomb and Welch conjectured that there does not exist perfect Lee code in Z with radius r ≥ 2 and dimension n ≥ 3. Besides its own interest in coding theory and discrete geometry, this conjecture is also strongly related to the degree-diameter problems of abelian Cayley graphs. Although there are many papers on this topic, the Golomb-Welch conjecture is far from being solved. In this ...

متن کامل

On the Minimum Length of some Linear Codes of Dimension 5

One of the interesting problems in coding theory is to determine the valuenq(k, d) which denotes the smallest number n such that an [n, k,d]q code existsfor given k, d and q.For k ≤ 5, there are many results for q ≤ 5 and for k = 6, the results areconcentrated in the ternary code ([1],[3]). In this talk, we concentrated in theproblem to find the exact value nq(6, d)....

متن کامل

Constacyclic Codes over Group Ring (Zq[v])/G

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

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

New minimum distance bounds for linear codes over GF(5)

Let [n; k; d]q-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, 32 new codes over GF(5) are constructed and the nonexistence of 51 codes is proved. c © 2003 Elsevier B.V. All rights reserved.

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:
  • Discrete Mathematics

دوره 238  شماره 

صفحات  -

تاریخ انتشار 2001