In order to minimize the number of orbits that must be enumerated or
represented, and following SLEPIAN again, we can restrict attention to
indecomposable linear 
-codes. Let 
be a linear
-code over 
with generator matrix 
and let 
be a linear 
-code over with generator matrix 
,
then the code 
with generator matrix
is called the direct sum of the codes and , and it will be
denoted by 
. A code is called decomposable, if
and only if it is equivalent to a code which is the direct sum of two or more
linear codes. Otherwise it is called indecomposable.
Since there are some errors in
SLEPIAN's table of the numbers of isometry classes
of indecomposable -codes, denoted by 
or 
,
the following theorem is proved in [5]:
This formula is implemented in SYMMETRICA as well. For instance for computing
the tables of 
and
one can use the next program:
INT co_all_codes()
{
OP n,k,q,R,S;
INT i,j;
INT erg=OK;
n=callocobject();
k=callocobject();
q=callocobject();
S=callocobject();
R=callocobject();
erg+=printeingabe("maximum value of n=? ");
erg+=scan(INTEGER,n);
erg+=printeingabe("maximum value of k=? ");
erg+=scan(INTEGER,k);
erg+=printeingabe("q=? ");
erg+=scan(INTEGER,q);
erg+=all_codes(n,k,q,S,R);
erg+=println(S);
erg+=println(R);
erg+=freeall(n); erg+=freeall(k); erg+=freeall(q);
erg+=freeall(S); erg+=freeall(R);
if (erg!=OK) return error(" in computation of co_all_codes");
return erg;
}
The routine all_codes(n,k,q,S,R) first computes the numbers
for 
and 
by (1),
then the 
by (2) and
finally the 
by (5). For computing the numbers of
classes of injective linear -codes by (3), (4) and (5)
there is the routine all_inj_codes(n,k,q,S,R).
The following tables
for 
, 
and 
were computed using these two routines:
Table 1: Number of isometry classes of linear -codes over 
Table 2: Number of isometry classes of indecomposable linear
-codes over
Table 3: Number of isometry classes of injective linear -codes over
Table 4: Number of isometry classes of injective
indecomposable linear -codes over
In [5] there are tables of and
for 
. Tables of can be found in [4][3]
and in the article of WILD [12], when interpreting matroids
as linear codes.
Extensions of the tables given in
[11] for the binary case were evaluated by LATTERMANN in
[10].
In her thesis [1],
ARNOLD evaluated transversals of isometry classes of linear codes. Another
implementation, due to BETTEN allowed to evaluate representatives of
all the isometry classes of indecomposable binary -codes for 
except for the case of 
and 
. Use was made of orderly generation
in connection with isomorphism checking [2].
Details will be given elsewhere.