MinT - Information on Result #670345

Information on Result #670345

Linear OA(81³⁶, 234, F₈₁, 21) (dual of [234, 198, 22]-code), using (u,Â u+v)-construction based on

linear OA(81¹², 116, F₈₁, 10) (dual of [116, 104, 11]-code), using
- extended algebraic-geometric code AG_e(F,105P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
  - a function field by SÃ©mirat [i]
linear OA(81²⁴, 118, F₈₁, 21) (dual of [118, 94, 22]-code), using
- constructionÂ X applied to AG(F,93P) âŠ‚ AG(F,95P) [i] based on
  1. linear OA(81²³, 115, F₈₁, 21) (dual of [115, 92, 22]-code), using algebraic-geometric code AG(F,93P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116 (see above)
  2. linear OA(81²¹, 115, F₈₁, 19) (dual of [115, 94, 20]-code), using algebraic-geometric code AG(F,95P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116 (see above)
  3. linear OA(81¹, 3, F₈₁, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 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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