MinT - Information on Result #671115

Information on Result #671115

Linear OA(128⁵¹, 388, F₁₂₈, 29) (dual of [388, 337, 30]-code), using (u,Â u+v)-construction based on

linear OA(128¹⁸, 194, F₁₂₈, 14) (dual of [194, 176, 15]-code), using
- constructionÂ X applied to AG(F,176P) âŠ‚ AG(F,178P) [i] based on
  1. linear OA(128¹⁷, 191, F₁₂₈, 14) (dual of [191, 174, 15]-code), using algebraic-geometric code AG(F,176P) [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(128¹⁵, 191, F₁₂₈, 12) (dual of [191, 176, 13]-code), using algebraic-geometric code AG(F,178P) [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(128³³, 194, F₁₂₈, 29) (dual of [194, 161, 30]-code), using
- constructionÂ X applied to AG(F,161P) âŠ‚ AG(F,163P) [i] based on
  1. linear OA(128³², 191, F₁₂₈, 29) (dual of [191, 159, 30]-code), using algebraic-geometric code AG(F,161P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (see above)
  2. linear OA(128³⁰, 191, F₁₂₈, 27) (dual of [191, 161, 28]-code), using algebraic-geometric code AG(F,163P) [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) (see above)

Mode: Constructive and linear.

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None.