Coding Theory
Magma provides comprehensive coding theory - linear codes over finite fields and rings, quantum stabiliser codes, minimum distance computation, decoding algorithms, and an extensive code database.
Contributors
A package for constructing linear codes associated with lattice points in a convex polytope has been contributed by Gavin Brown (Loughborough) and Alexander Kasprzyk (Imperial).
The PERM package developed by Jeff Leon (UIC) is used to determine automorphism groups of codes, designs and matrices.
The development of machinery for linear codes benefited greatly from the active involvement of Markus Grassl (Karlsruhe) over a long period. Of particular note is his contribution to the development of improved algorithms for computing the minimum weight and for the enumeration of codewords.
Routines implementing many different constructions for linear codes over finite fields were contributed by Markus Grassl (Karlsruhe).
Markus Grassl (Karlsruhe) played a key role in the design of Magma packages for additive codes and quantum error-correcting codes. The packages were implemented by Greg White (Magma).
The construction of a database of best known linear codes over GF(2) was a joint project with Markus Grassl (Karlsruhe, NUS). Other contributors to this project include: Andries Brouwer, Zhi Chen, Stephan Grosse, Aaron Gulliver, Ray Hill, David Jaffe, Simon Litsyn, James Shearer, and Henk van Tilborg.
The databases of best known linear codes over GF(3), GF(4), GF(5), GF(7), GF(8) and GF(9) were constructed by Markus Grassl (IAKS, Karlsruhe).
A substantial collection of intrinsics for constructing and computing properties of ℤ4 codes, building on Magma's basic machinery for Z4 codes, was contributed in 2009 by the Combinatoric, Coding and Security Group (CCSG) at the Universitat Autònoma de Barcelona headed by Merc Villanueva. The other members of the group were Roland D. Barrolleta, Jaume Pernas, and Jaume Pujol. They subsequently extended the package to include automorphism groups of ℤ4 codes and a range of decoding algorithms. This version was released in 2016 with Magma V2.22.
Code for permutation decoding of linear codes over Fq was contributed by the CCSG group (Universitat Autònoma de Barcelona) in 2016.