MinT - Information on Result #668329

Information on Result #668329

Linear OA(32¹⁰², 1103, F₃₂, 40) (dual of [1103, 1001, 41]-code), using (u,Â u+v)-construction based on

linear OA(32²⁶, 78, F₃₂, 20) (dual of [78, 52, 21]-code), using
- constructionÂ X applied to AG(F,54P) âŠ‚ AG(F,56P) [i] based on
  1. linear OA(32²⁵, 75, F₃₂, 20) (dual of [75, 50, 21]-code), using algebraic-geometric code AG(F,54P) [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]
  2. linear OA(32²³, 75, F₃₂, 18) (dual of [75, 52, 19]-code), using algebraic-geometric code AG(F,56P) [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76 (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(32⁷⁶, 1025, F₃₂, 40) (dual of [1025, 949, 41]-code), using
- the BCH-code C(I) with length 1025Â | 32⁴âˆ’1, defining interval IÂ =Â {−1,367,735,…,1}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]

Mode: Constructive and linear.

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