MinT - Information on Result #629617

Information on Result #629617

Linear OA(2²²⁹, 280, F₂, 71) (dual of [280, 51, 72]-code), using concatenation of two codes based on

linear OA(8⁵³, 70, F₈, 35) (dual of [70, 17, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁵³, 73, F₈, 35) (dual of [73, 20, 36]-code), using
  - constructionÂ X applied to AG(F,28P) âŠ‚ AG(F,33P) [i] based on
    1. linear OA(8⁴⁹, 64, F₈, 35) (dual of [64, 15, 36]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]
    2. linear OA(8⁴⁴, 64, F₈, 30) (dual of [64, 20, 31]-code), using algebraic-geometric code AG(F,33P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    3. linear OA(8⁴, 9, F₈, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,8)), using
      - extended Reedâ€“Solomon code RS_e(5,8) [i]
linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Constructive and linear.

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