Is there a location where one can access generator matrices (not just bounds) of best known linear codes?
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$\begingroup$ Here (with Magma): dms.umontreal.ca/~math/Logiciels/Magma/text1571.htm $\endgroup$– Dietrich BurdeCommented Aug 5, 2013 at 12:19
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$\begingroup$ Does this system have to be installed? Or is there an online query system? $\endgroup$– TurboCommented Aug 5, 2013 at 12:25
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1$\begingroup$ magma.maths.usyd.edu.au/calc/. $\endgroup$– Dietrich BurdeCommented Aug 5, 2013 at 18:33
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$\begingroup$ Thnakyou. This helped. You could make this as an answer. I could close the question. $\endgroup$– TurboCommented Aug 6, 2013 at 7:06
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1 Answer
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There is a Magma BKLC (Best Known Linear Codes, i.e., linear $[n,k,d]_q$-codes, which have the highest minimum weight among all known linear $[n, k,d]_q$-codes)
database. It contains also generator matrices.
The construction of this Magma BKLC database has been undertaken by John Cannon (Sydney), Markus Grassl (Karlsruhe) and Greg White (Sydney). For references, examples and the online Magma calculator see the links given in the comments.
Perhaps also interesting is the page on "best linear codes", http://www.algorithm.uni-bayreuth.de/en/research/Coding_Theory/Linear_Codes_BKW/, which contains recently found new best linear codes.
answered Aug 6, 2013 at 8:31