MinT - Information on Result #671077

Information on Result #671077

Linear OA(128⁵⁵, 386, F₁₂₈, 32) (dual of [386, 331, 33]-code), using (u,Â u+v)-construction based on

linear OA(128¹⁹, 192, F₁₂₈, 16) (dual of [192, 173, 17]-code), using
- extended algebraic-geometric code AG_e(F,175P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
  - a function field by SÃ©mirat [i]
linear OA(128³⁶, 194, F₁₂₈, 32) (dual of [194, 158, 33]-code), using
- constructionÂ X applied to AG(F,158P) âŠ‚ AG(F,160P) [i] based on
  1. linear OA(128³⁵, 191, F₁₂₈, 32) (dual of [191, 156, 33]-code), using algebraic-geometric code AG(F,158P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (see above)
  2. linear OA(128³³, 191, F₁₂₈, 30) (dual of [191, 158, 31]-code), using algebraic-geometric code AG(F,160P) [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]

Mode: Constructive and linear.

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