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Table 1 Upper bounds for the dimension k of linear Lee codes when \(q=5\)

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*

             

0.007

3

1*

1*

            

0.013

4

2*

2*

1*

1*

          

0.026

5

3*

3*

2*

1*

1*

         

0.041

6

4*

3*

3*

2*

1*

1*

1*

       

0.068

7

5*

4*

3*

3*

2*

1*

1*

1*

      

0.102

8

6*

5*

4*

4*

3*

2*

2*

1*

1*

1*

    

0.169

9

7*

6*

5*

5

4*

3*

3

2*

1*

1*

1*

   

0.249

10

8*

7*

6*

6

5

4

3*

3

2*

2*

1*

1*

1*

 

0.408

11

9*

8*

7

6*

6

5

4

4

3

2*

2*

1*

1*

1*

0.563

12

10*

9*

8

7

7

6

5

5

4

3*

2*

2*

2*

1*

 

13

10*

10*

9

8

7

7

6

5

5

4

3*

2*

2*

1*

 

14

11*

11

10

9

8

8

7

6

5

5

4

3*

3

2*

 

15

12*

12

11

10

9

9

8

7

6

6

5

4

4

3

 

n\d

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Time [s]

12

1*

1*

            

0.872

13

1*

1*

1*

           

1.426

14

1*

1*

1*

1*

1*

         

2.517

15

2*

2*

1*

1*

1*

1*

        

3.951

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