Geodesic
The number of inequivalent \((2R+3,7)R\) optimal covering codes
Journal of integer sequences, Tome 9 (2006) no. 4
Let $(n,M)R$ denote any binary code with length $n$, cardinality $M$ and covering radius $R$. The classification of $(2R+3,7)R$ codes is settled for any $R=1,2,\dots $, and a characterization of these (optimal) codes is obtained. It is shown that, for $R=1,2,\dots $, the numbers of inequivalent $(2R+3,7)R$ codes form the sequence 1,3,8,17,33,$\dots $identified as A002625 in the Encyclopedia of Integer Sequences and given by the coefficients in the expansion of 1/$((1-x)^{3}(1-x^{2})^{2}(1-x^{3}))$.
Classification : 94B75, 05B40, 94B25
Keywords: covering radius 
@article{JIS_2006__9_4_a1,
     author = {K\'eri,  Gerzson and \"Osterg\r{a}rd,  Patric R.J.},
     title = {The number of inequivalent {\((2R+3,7)R\)} optimal covering codes},
     journal = {Journal of integer sequences},
     year = {2006},
     volume = {9},
     number = {4},
     zbl = {1104.94063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_4_a1/}
}
TY  - JOUR
AU  - Kéri,  Gerzson
AU  - Östergård,  Patric R.J.
TI  - The number of inequivalent \((2R+3,7)R\) optimal covering codes
JO  - Journal of integer sequences
PY  - 2006
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JIS_2006__9_4_a1/
LA  - en
ID  - JIS_2006__9_4_a1
ER  - 
%0 Journal Article
%A Kéri,  Gerzson
%A Östergård,  Patric R.J.
%T The number of inequivalent \((2R+3,7)R\) optimal covering codes
%J Journal of integer sequences
%D 2006
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/JIS_2006__9_4_a1/
%G en
%F JIS_2006__9_4_a1
Kéri,  Gerzson; Östergård,  Patric R.J. The number of inequivalent \((2R+3,7)R\) optimal covering codes. Journal of integer sequences, Tome 9 (2006) no. 4. http://geodesic.mathdoc.fr/item/JIS_2006__9_4_a1/