MinT - Information on Result #671067

Information on Result #671067

Linear OA(128⁵⁸, 410, F₁₂₈, 33) (dual of [410, 352, 34]-code), using (u,Â u+v)-construction based on

linear OA(128²⁰, 194, F₁₂₈, 16) (dual of [194, 174, 17]-code), using
- constructionÂ X applied to AG(F,174P) âŠ‚ AG(F,176P) [i] based on
  1. linear OA(128¹⁹, 191, F₁₂₈, 16) (dual of [191, 172, 17]-code), using algebraic-geometric code AG(F,174P) [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(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 (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(128³⁸, 216, F₁₂₈, 33) (dual of [216, 178, 34]-code), using
- extended algebraic-geometric code AG_e(F,182P) [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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