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I need the characterization (up to isomorphism) of non-commutative local rings (with identity) of orders 64 and 128. If you know the characterization or a reference, please let me know.

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  • $\begingroup$ Dear @nikitar: As it stands, in your sentence "... orders 64 and 128 and." it appears you wanted to write at least one more number. Is that correct? On a different note, the tag 'local-rings' might be more appropriate than the tag 'finite-fields'. $\endgroup$ – Ricardo Andrade Sep 9 '13 at 13:47
  • $\begingroup$ @RicardoAndrade The second "and" was a mistype. Thanks for mentioning it. $\endgroup$ – nikitar Sep 9 '13 at 18:00
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At the end of the article

A.Z.Anan'in, On representability of a finite local ring, J. of Algebra 228 (2000), no. 2, 417--427 (see also Mathematical Reviews 01i:14018),

it is mentioned that the minimal size of "unknown" finite noncommutative local ring is 256. I mean that one can derive the answer by following constructions presented in the article. Sorry for this incomplete answer: I have no rights to write a comment, whereas a complete answer would require some addtional effort (and I am too lazy for that at the moment).

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