MinT - Information on Result #668885

Information on Result #668885

Linear OA(32⁷¹, 1048622, F₃₂, 16) (dual of [1048622, 1048551, 17]-code), using (u,Â u+v)-construction based on

linear OA(32¹⁰, 46, F₃₂, 8) (dual of [46, 36, 9]-code), using
- constructionÂ X applied to AG(F,34P) âŠ‚ AG(F,36P) [i] based on
  1. linear OA(32⁹, 43, F₃₂, 8) (dual of [43, 34, 9]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
    - a function field by SÃ©mirat [i]
  2. linear OA(32⁷, 43, F₃₂, 6) (dual of [43, 36, 7]-code), using algebraic-geometric code AG(F,36P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44 (see above)
  3. linear OA(32¹, 3, F₃₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(32⁶¹, 1048576, F₃₂, 16) (dual of [1048576, 1048515, 17]-code), using
- an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

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