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A [45, 13] Code with Minimal Distance 16

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by

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J.H. Conway

S.J. Lomonaco, Jr.

N.J.A. Sloane

**ABSTRACT.**

**A record code of length 45,
dimension 13
and minimal distance 16
is constructed in several ways: as an Abelian code (an ideal in the regular
representation of C**_{3} X C_{15})
, from a [15,6,8]
cyclic code over GF(4) ,
and from the | a+x | b+x | c+x |
construction. Its automorphism group has order 360,
and its even sucode is a [45,12,16]
code with only four nonzero weights.