MinT - Information on Result #663600

Information on Result #663600

Linear OA(8¹²⁶, 540, F₈, 39) (dual of [540, 414, 40]-code), using (u,Â u+v)-construction based on

linear OA(8²³, 27, F₈, 19) (dual of [27, 4, 20]-code), using
- constructionÂ X applied to AG(F,2P) âŠ‚ AG(F,3P) [i] based on
  1. linear OA(8²², 24, F₈, 19) (dual of [24, 2, 20]-code), using algebraic-geometric code AG(F,2P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F₈ [i]
  2. linear OA(8²⁰, 24, F₈, 17) (dual of [24, 4, 18]-code), using algebraic-geometric code AG(F,3P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24 (see above)
  3. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(8¹⁰³, 513, F₈, 39) (dual of [513, 410, 40]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513Â | 8⁶âˆ’1, defining interval IÂ =Â [0,19], and minimum distance dÂ â‰¥ |{−19,−18,…,19}|+1Â =Â 40 (BCH-bound) [i]

Mode: Constructive and linear.

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