MinT - Information on Result #668371

Information on Result #668371

Linear OA(32¹⁰⁴, 1149, F₃₂, 38) (dual of [1149, 1045, 39]-code), using (u,Â u+v)-construction based on

linear OA(32³², 124, F₃₂, 19) (dual of [124, 92, 20]-code), using
- constructionÂ X applied to AG(F,99P) âŠ‚ AG(F,102P) [i] based on
  1. linear OA(32³⁰, 119, F₃₂, 19) (dual of [119, 89, 20]-code), using algebraic-geometric code AG(F,99P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]
  2. linear OA(32²⁷, 119, F₃₂, 16) (dual of [119, 92, 17]-code), using algebraic-geometric code AG(F,102P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120 (see above)
  3. linear OA(32², 5, F₃₂, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,32)), using
    - discarding factors / shortening the dual code based on linear OA(32², 32, F₃₂, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
      - Reedâ€“Solomon code RS(30,32) [i]
linear OA(32⁷², 1025, F₃₂, 38) (dual of [1025, 953, 39]-code), using
- the BCH-code C(I) with length 1025Â | 32⁴âˆ’1, defining interval IÂ =Â {32,335,638,…,−32}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]

Mode: Constructive and linear.

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