MinT - Information on Result #658919

Information on Result #658919

Linear OA(8⁶⁴, 79, F₈, 43) (dual of [79, 15, 44]-code), using constructionÂ XX applied to AG(F,20P) âŠ‚ AG(F,26P) âŠ‚ AG(F,28P) based on

linear OA(8⁵⁶, 64, F₈, 43) (dual of [64, 8, 44]-code), using algebraic-geometric code AG(F,20P) 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(8⁵⁰, 64, F₈, 37) (dual of [64, 14, 38]-code), using algebraic-geometric code AG(F,26P) 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, 13, F₈, 5) (dual of [13, 7, 6]-code), using
- discarding factors / shortening the dual code based on 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(8¹, 2, F₈, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]

Mode: Constructive and linear.

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