MinT - Information on Result #906655

Information on Result #906655

Linear OOA(8¹⁶³, 84, F₈, 2, 139) (dual of [(84, 2), 5, 140]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8²⁰, 12, F₈, 2, 19) (dual of [(12, 2), 4, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8²⁰, 14, F₈, 2, 19) (dual of [(14, 2), 8, 20]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;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 OOA(8²³, 12, F₈, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
- dual of repetition NRT-code with length 12 [i]
linear OOA(8²⁴, 12, F₈, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(8²⁴, 12, F₈, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)
linear OOA(8²⁴, 12, F₈, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)
linear OOA(8²⁴, 12, F₈, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)
linear OOA(8²⁴, 12, F₈, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)

Mode: Constructive and linear.

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