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Table 2 Upper bounds for the dimension k of linear Lee codes when \(q=7\)

From: On the linear programming bound for linear Lee codes

n\d

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Time [s]

2

1*

             

0.009

3

2*

1*

1*

1*

          

0.028

4

2*

2*

2*

1*

1*

         

0.047

5

3*

3*

2*

2*

1*

1*

1*

       

0.098

6

4*

4*

3*

3*

2*

2*

1*

1*

1*

1*

    

0.212

7

5*

5*

4*

4

3*

3

2*

2*

1*

1*

1*

   

0.420

8

6*

5*

5*

4*

4*

4

3*

3

2*

2*

1*

1*

1*

 

0.816

9

7*

6*

6

5*

5

4*

4

3*

3

3

2*

1*

1*

1*

 

10

8*

7*

7

6*

6

5

5

4

4

3*

3

2*

2*

1*

 

11

9*

8*

8

7

6*

5

5

5

5

4

4

3

3

2*

 

12

10*

9*

8*

8

7

7

6

6

5

5

4

4

3

3

 

13

11*

10*

9*

9

8

8

7

7

6

6

5

5

4

4

 

14

12*

11*

10*

10

9

9

8

8

7

7

6

6

5

5

 

15

13*

12*

11*

11

10

10

9

9

8

7

7

6

6

5

 

n\d

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Time [s]

9

1*

1*

            

1.621

10

1*

1*

1*

           

2.959

11

2*

2

1*

1*

1*

         

6.406

12

3

2*

2

1*

1*

1*

1*

1*

      

17.580

13

3

3

2*

2*

2

1*

1*

1*

1*

     

31.983

14

4

4

3

3

2*

2*

2

1*

1*

1*

1*

   

67.885

15

5

5

4

4

3

3

2*

2*

1*

1*

1*

1*

1*

1*

173.448

  1. The * indicates a tight bound and italics an improvement compared to the bound given by (2)
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