On The Classification of Binary Optimal Self-Orthogonal Codes

The classification of binary [
n
,
k
,
d
] codes with
d
ges
s
2
k
-1 and without zero coordinates is reduced to the classification of binary [(2
k
-1)
c
(
k
,
s
,
t
)+
t
,
k
,
d
] code for
n
=(2
k
-1)
s
+
t
,
s
ges 1 and 1 les
t
les 2
k
-2, where
c
(
k
,
s
,
t
) les min{
s
,
t
} is a function of
k
,
s
, and
t
. Binary [15
s
+
t
, 4] optimal self-orthogonal codes are characterized by systems of linear equations. Based on these two results, the complete classification of [15
s
+
t
,4] optimal self-orthogonal codes for
t
isin {1,2,6,7,8,9,13,14} and
s
ges 1 is obtained, and the generator matrices and weight polynomials of these 4-dimensional optimal self-orthogonal codes are also given.