MinT - Information on Result #668621

Information on Result #668621

Linear OA(32⁶⁵, 1091, F₃₂, 25) (dual of [1091, 1026, 26]-code), using (u,Â u+v)-construction based on

linear OA(32¹⁶, 66, F₃₂, 12) (dual of [66, 50, 13]-code), using
- constructionÂ X applied to AG(F,50P) âŠ‚ AG(F,52P) [i] based on
  1. linear OA(32¹⁵, 63, F₃₂, 12) (dual of [63, 48, 13]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]
  2. linear OA(32¹³, 63, F₃₂, 10) (dual of [63, 50, 11]-code), using algebraic-geometric code AG(F,52P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64 (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(32⁴⁹, 1025, F₃₂, 25) (dual of [1025, 976, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025Â | 32⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Constructive and linear.

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