MinT - Information on Result #663614

Information on Result #663614

Linear OA(8¹¹², 540, F₈, 35) (dual of [540, 428, 36]-code), using (u,Â u+v)-construction based on

linear OA(8²¹, 27, F₈, 17) (dual of [27, 6, 18]-code), using
- constructionÂ X applied to AG(F,3P) âŠ‚ AG(F,4P) [i] based on
  1. 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, using the Klein quartic over F₈ [i]
  2. linear OA(8¹⁸, 24, F₈, 15) (dual of [24, 6, 16]-code), using algebraic-geometric code AG(F,4P) 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(8⁹¹, 513, F₈, 35) (dual of [513, 422, 36]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513Â | 8⁶âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]

Mode: Constructive and linear.

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