Introduction

This is a database of self-dual quantum codes over GF(3), GF(4), and GF(5). These can also be interpreted as classical self-dual additive codes over GF(9), GF(16), and GF(25). For a classification of binary quantum codes (self-dual additive codes over GF(4)), see the Database of Self-Dual Quantum Codes.

These codes were classified by using the fact that they can be represented as weighted graphs. For details, see the paper [1].

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Tables

Total number of self-dual quantum codes over GF(m) (self-dual additive codes over GF(m²)) of length n:

m\n	1	2	3	4	5	6	7	8	9	10	11	12
2	1	2	3	6	11	26	59	182	675	3,990	45,144	1,323,363
3	1	2	3	7	13	39	121	817
4	1	2	3	7	14	44
5	1	2	3	7	15	58

Number of indecomposable self-dual quantum codes over GF(3) (self-dual additive codes over GF(9)) of length n and distance d:

d\n	2	3	4	5	6	7	8	9	10
2	1	1	2	4	15	51	388	?	?
3			1	1	5	20	194	?	?
4					1	2	77	?	?
5								4	?
6									1
All	1	1	3	5	21	73	659	?	?

Number of indecomposable self-dual quantum codes over GF(4) (self-dual additive codes over GF(16)) of length n and distance d:

d\n	2	3	4	5	6
2	1	1	2	4	16
3			1	2	6
4					3
5
6
All	1	1	3	6	25

Number of indecomposable self-dual quantum codes over GF(5) (self-dual additive codes over GF(25)) of length n and distance d:

d\n	2	3	4	5	6
2	1	1	2	4	21
3			1	3	11
4					6
5
6
All	1	1	3	7	38

See the paper [1] for more tables and information.

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Files

There is one file for codes over each alphabet. The records have the following format:

• length of code
• minimum distance of code
• LC orbit size
• weighted graph representation of code (Example: the graph "03,2*13,3*23" has edge {0,3} with weight 1, edge {1,3} with weight 2, and edge {2,3} with weight 2.)

m	Download
3	selfdualcodes3.txt
4	selfdualcodes4.txt
5	selfdualcodes5.txt

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References

[1] Lars Eirik Danielsen and Matthew G. Parker: Graph-based classification of self-dual additive codes over finite fields, October 2007.