MinT - Information on Result #670887

Information on Result #670887

Linear OA(128⁷⁸, 410, F₁₂₈, 46) (dual of [410, 332, 47]-code), using (u,Â u+v)-construction based on

linear OA(128²⁷, 194, F₁₂₈, 23) (dual of [194, 167, 24]-code), using
- constructionÂ X applied to AG(F,167P) âŠ‚ AG(F,169P) [i] based on
  1. linear OA(128²⁶, 191, F₁₂₈, 23) (dual of [191, 165, 24]-code), using algebraic-geometric code AG(F,167P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]
  2. linear OA(128²⁴, 191, F₁₂₈, 21) (dual of [191, 167, 22]-code), using algebraic-geometric code AG(F,169P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (see above)
  3. linear OA(128¹, 3, F₁₂₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(128⁵¹, 216, F₁₂₈, 46) (dual of [216, 165, 47]-code), using
- extended algebraic-geometric code AG_e(F,169P) [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
  - a function field by SÃ©mirat [i]

Mode: Constructive and linear.

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