On the covering radius of small codes

被引：0
|
作者：
Kéri, G
Östergård, PRJ
机构：
[1] Hungarian Acad Sci, Szamitastech & Automat Kutato Intezet, H-1518 Budapest, Hungary
[2] Helsinki Univ Technol, Dept Elect & Commun Engn, Sahko Ja Tietoliikennetekniikan Osasto Teknilline, SF-02015 Espoo 15, Finland
来源：
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2003年 / 40卷 / 1-2期
关键词：
covering code; covering radius; mixed code; surjective code;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The minimum number of codewords in a code with t, ternary and b binary coordinates and covering radius R is denoted by K(t, b, R). In this paper, necessary and sufficient conditions for K(t, b, R) = M are given for all M less than or equal to 5. By the help of generalized s-surjective codes, we develop new methods for finding bounds for K(t, b, R). These results are used to prove the equality K(9, 0, 5) = 6 as well as some new lower bounds such as K(2, 7,3) greater than or equal to 7, K(3, 6, 3) greater than or equal to 8, K(5, 3, 3) greater than or equal to 8, and K(9, 0, 4) greater than or equal to 9. Some bounds for (nonmixed) quaternary codes are also obtained.
引用
收藏
页码：243 / 256
页数：14
相关论文
共 50 条
  • [41] CONSTRUCTIONS OF CODES WITH COVERING RADIUS-2
    DAVYDOV, AA
    LECTURE NOTES IN COMPUTER SCIENCE, 1992, 573 : 23 - 31
  • [42] FURTHER RESULTS ON THE COVERING RADIUS OF CODES.
    Cohen, Gerard D.
    Lobstein, Antoine C.
    Sloane, N.J.A.
    IEEE Transactions on Information Theory, 1986, IT-32 (06) : 680 - 694
  • [43] Resolution of a Conjecture on the Covering Radius of Linear Codes
    Orozco, Juan Carlos
    Janwa, Heeralal
    COMBINATORICS, GRAPH THEORY AND COMPUTING, SEICCGTC 2021, 2024, 448 : 413 - 425
  • [44] COVERING RADIUS COMPUTATIONS FOR BINARY CYCLIC CODES
    DOUGHERTY, R
    JANWA, H
    MATHEMATICS OF COMPUTATION, 1991, 57 (195) : 415 - 434
  • [45] ON THE COVERING RADIUS OF SOME BINARY CYCLIC CODES
    Arce-Nazario, Rafael
    Castro, Francis N.
    Ortiz-Ubarri, Jose
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2017, 11 (02) : 329 - 338
  • [46] Density of constant radius normal binary covering codes
    Ellis, Robert B.
    DISCRETE MATHEMATICS, 2008, 308 (19) : 4446 - 4459
  • [47] On the covering radius of Z4-codes and their lattices
    Aoki, T
    Gaborit, P
    Harada, M
    Ozeki, M
    Solé, P
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (06) : 2162 - 2168
  • [48] The covering radius of some primitive ternary BCH codes
    Franken, R
    Cohen, SD
    FINITE FIELDS AND APPLICATIONS, 2004, 2948 : 166 - 180
  • [49] Method to calculate the covering radius for linear block codes
    Elektrosvyaz, 8 (19-20):
  • [50] THE COVERING RADIUS OF CYCLIC CODES OF LENGTH UP TO 31
    DOWNIE, DE
    SLOANE, NJA
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1985, 31 (03) : 446 - 447
12345