8.28 Coding Theory (10.12.99)

8.28.1 John Ryan

Has anyone ever written a procedure in MAPLE to check if two codes (Error Correcting Codes) are equivalent? If so I would be very very interested.

8.28.2 David Joyner (16.12.99)

My little package

http://web.usna.navy.mil/~wdj/codes.htm

doesn’t do that but I think it would be very easy to write a program which would simply compare generator matrices for *binary* linear codes.

GAP has a package (guava) which does such things in general.

8.28.3 Brendan McKay (21.12.99)

If "equivalance" permits the relabelling of coordinate dimensions (i.e. the rows, if the generators are written as columns), then it is a very hard problem.

The best code that I know of is due to Jeffrey Leon (in C). It is available in Magma; not sure about GAP. It would run very slowly if implemented directly in Maple.

8.28.4 David Joyner (6.1.00)

I have updated the coding theory package at

http://web.usna.navy.mil/~wdj/codes.html

to include a procedure to determine if two binary linear codes are equivalent.

Also, I added a program to compute the automorphism group of a binary linear code. This addition requires the group2.1 package at

http://web.usna.navy.mil/~wdj/symm_gp.html

It won’t be fast but it is useful for teaching and explaining examples to students.

The GAP package guava (see http://mirrors.ccs.neu.edu/GAP/NEU/Manual/C065S000.htm) Prof McKay mentioned in his recent MUG post is not, according to the GAP support team, available under windows.