MinT - Information on Result #670983

Information on Result #670983

Linear OA(128⁶⁷, 410, F₁₂₈, 39) (dual of [410, 343, 40]-code), using (u,Â u+v)-construction based on

linear OA(128²³, 194, F₁₂₈, 19) (dual of [194, 171, 20]-code), using
- constructionÂ X applied to AG(F,171P) âŠ‚ AG(F,173P) [i] based on
  1. linear OA(128²², 191, F₁₂₈, 19) (dual of [191, 169, 20]-code), using algebraic-geometric code AG(F,171P) [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(128²⁰, 191, F₁₂₈, 17) (dual of [191, 171, 18]-code), using algebraic-geometric code AG(F,173P) [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(128⁴⁴, 216, F₁₂₈, 39) (dual of [216, 172, 40]-code), using
- extended algebraic-geometric code AG_e(F,176P) [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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