A note on bounds for q-ary covering codes
نویسندگان
چکیده
Two strongly seminormal codes over 2s are constructed to prove a conjecture of Ostergard. It is shown that a result of Honkala on ( I C , t)-subnormal codes holds also under weaker assumptions. A lower bound and an upper bound on Kq(n, R), the minimal cardinality of a q-ary code of length n with covering radius R are obtained. These give improvements in seven upper bounds and twelve lower bounds by Ostergard for K,(n, R) for q = 3, 4, and 5. seminormal codes, g-ary codes. I
منابع مشابه
New Constructions for q-ary Covering Codes
Upper bounds on Kq (n; R), the minimum number of codewords in a q-ary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance separable (MDS) codes. Furthermore, they can often be combined eeectively with other covering co...
متن کاملLinear codes with covering radius 3
The shortest possible length of a q-ary linear code of covering radius R and codimension r is called the length function and is denoted by q(r, R). Constructions of codes with covering radius 3 are here developed, which improve best known upper bounds on q(r, 3). General constructions are given and upper bounds on q(r, 3) for q = 3, 4, 5, 7 and r ≤ 24 are tabulated.
متن کاملA Note On Covering Radius Of Macdonald Codes
In this paper we determine an upper bound for the covering radius of a q-ary MacDonald codeCk;u(q). Values of nq(4; d), the minimal length of a 4-dimensional q-ary code with minimum distance d is obtained for d = q 1 and q 2. These are used to determine the covering radius of C3;1(q),C3;2(q) and C4;2(q).
متن کاملNew Bounds for Linear Codes of Covering Radius 2
The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that
متن کاملOn new completely regular q-ary codes
In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...
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:
- IEEE Trans. Information Theory
دوره 42 شماره
صفحات -
تاریخ انتشار 1996