MinT - Information on Result #661597

Information on Result #661597

Linear OA(8⁷⁹, 84, F₈, 64) (dual of [84, 5, 65]-code), using juxtaposition based on

linear OA(8⁹, 14, F₈, 8) (dual of [14, 5, 9]-code), using
- extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
  - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
linear OA(8⁶⁵, 70, F₈, 55) (dual of [70, 5, 56]-code), using
- constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(8⁶¹, 64, F₈, 55) (dual of [64, 3, 56]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [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(8⁵⁹, 64, F₈, 50) (dual of [64, 5, 51]-code), using algebraic-geometric code AG(F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)), using
    - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
      - Reedâ€“Solomon code RS(4,8) [i]

Mode: Constructive and linear.

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