Linear Codes over Finite Fields [HB 115]

New Features:

• The Best Known Linear Codes package now includes a database of codes over GF(3). This database is a contribution of Markus Grassl, Karlsruhe. The database is completely full up to length 100, providing 5, 150 codes. The codes of length up to 21 are optimal. The database over GF(4) is now over 99% complete, with only 40 of the 5, 150 codes missing.

• New packing methods, developed by Greg White, have resulted in faster vector addition for small non-binary finite fields. Vector enumeration is the core operation in almost all important computations in coding theory, such as calculating the minimum weight, the weight distribution, or the complete weight enumerator. For the finite fields GF(3), GF(4) and GF(8) there has been a factor of 3 - 4 scalar speed up for all of these computations.

• The important minimum weight algorithm has been improved in various ways. This includes the use of a finer incrementing of the lower bound, which allows some computations to finish several steps earlier then before. Since the bulk of the computation is done in the final steps this causes a huge speed up for certain cases. Also, revolving door algorithms have been used in the vector enumeration resulting in about 20% reduction in the number of vector operations.

• The minimum weight algorithm has a new verbose output with several improvements. A useful new feature is an accurate prediction of not only the stage, but also the time at which the algorithm will finish.