MinT - Information on Result #658912

Information on Result #658912

Linear OA(8⁶⁷, 82, F₈, 44) (dual of [82, 15, 45]-code), using constructionÂ XX applied to AG(F,18P) âŠ‚ AG(F,25P) âŠ‚ AG(F,28P) based on

linear OA(8⁵⁷, 64, F₈, 45) (dual of [64, 7, 46]-code), using algebraic-geometric code AG(F,18P) 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]
linear OA(8⁵¹, 64, F₈, 38) (dual of [64, 13, 39]-code), using algebraic-geometric code AG(F,25P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
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 (see above)
linear OA(8⁶, 14, F₈, 5) (dual of [14, 8, 6]-code), using
- extended algebraic-geometric code AG_e(F,8P) [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(8², 4, F₈, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,8)), using
- discarding factors / shortening the dual code based on linear OA(8², 8, F₈, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
  - Reedâ€“Solomon code RS(6,8) [i]

Mode: Constructive and linear.

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