MinT - Information on Result #909048

Information on Result #909048

Linear OOA(3¹²⁶, 69, F₃, 2, 72) (dual of [(69, 2), 12, 73]-NRT-code), using juxtaposition based on

linear OOA(3⁴², 27, F₃, 2, 27) (dual of [(27, 2), 12, 28]-NRT-code), using
- algebraic-geometric NRT-code AG(2;F,26P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁷², 42, F₃, 2, 44) (dual of [(42, 2), 12, 45]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷², 84, F₃, 44) (dual of [84, 12, 45]-code), using
  - constructionÂ X applied to C([0,87]) âŠ‚ C([0,81]) [i] based on
    1. linear OA(3⁷⁰, 80, F₃, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3¹⁵⁰, 160, F₃, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [0,87], and minimum distance dÂ â‰¥ |{−1,0,…,87}|+1Â =Â 90 (BCH-bound) [i]
    2. linear OA(3⁶⁶, 80, F₃, 41) (dual of [80, 14, 42]-code), using contraction [i] based on linear OA(3¹⁴⁶, 160, F₃, 83) (dual of [160, 14, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [0,81], and minimum distance dÂ â‰¥ |{−1,0,…,81}|+1Â =Â 84 (BCH-bound) [i]
    3. linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
      - extended Reedâ€“Solomon code RS_e(2,3) [i]
      - Hamming code H(2,3) [i]
      - Simplex code S(2,3) [i]
      - the Tetracode [i]

Mode: Constructive and linear.

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