The nonexistence of ternary [105, 6, 68] and [230, 6, 152] codes

نویسندگان

  • Rumen N. Daskalov
  • Elena Metodieva
چکیده

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, the nonexistence of [105, 6, 68]3 and [230, 6, 152]3 codes is proved. © 2004 Elsevier 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 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

Some New Optimal Ternary Linear Codes

Let d3(n, k) be the maximum possible minimum Hamming distance of a ternary [n, k, d; 3]-code for given values of n and k. It is proved that d3(44, 6) = 27, d3(76, 6) = 48, d3(94, 6) = 60, d3(124, 6) = 81, d3(130, 6) = 84, d3(134, 6) = 87, d3(138, 6) = 90, d3(148, 6) = 96, d3(152, 6) = 99, d3(156, 6) = 102, d3(164, 6) = 108, d3(170, 6) = 111, d3(179, 6) = 117, d3(188, 6) = 123, d3(206, 6) = 135,...

متن کامل

On Perfect Ternary Constant Weight Codes

We consider the space of ternary words of length n and fixed weightwwith the usual Hamming distance. A sequence of perfect single error correcting codes in this space is constructed. We prove the nonexistence of such codes with other parameters than those of the sequence.

متن کامل

On non-antipodal binary completely regular codes

Binary non-antipodal completely regular codes are characterized. Using the result on nonexistence of nontrivial binary perfect codes, it is concluded that there are no unknown nontrivial non-antipodal completely regular binary codes with minimum distance d ≥ 3. The only such codes are halves and punctered halves of known binary perfect codes. Thus, new such codes with covering radiuses ρ = 2, 3...

متن کامل

Ternary Code Construction of Unimodular Lattices and Self-Dual Codes over <Subscript>6</Subscript>

We revisit the construction method of even unimodular lattices using ternary self-dual codes given by the third author (M. Ozeki, in Théorie des nombres, J.-M. De Koninck and C. Levesque (Eds.) (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 772–784), in order to apply the method to odd unimodular lattices and give some extremal (even and odd) unimodular lattices explicitly. In passing we cor...

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 286  شماره 

صفحات  -

تاریخ انتشار 2004