MinT - Information on Result #670947

Information on Result #670947

Linear OA(128⁶⁹, 388, F₁₂₈, 41) (dual of [388, 319, 42]-code), using (u,Â u+v)-construction based on

linear OA(128²⁴, 194, F₁₂₈, 20) (dual of [194, 170, 21]-code), using
- constructionÂ X applied to AG(F,170P) âŠ‚ AG(F,172P) [i] based on
  1. linear OA(128²³, 191, F₁₂₈, 20) (dual of [191, 168, 21]-code), using algebraic-geometric code AG(F,170P) [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(128²¹, 191, F₁₂₈, 18) (dual of [191, 170, 19]-code), using algebraic-geometric code AG(F,172P) [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(128⁴⁵, 194, F₁₂₈, 41) (dual of [194, 149, 42]-code), using
- constructionÂ X applied to AG(F,149P) âŠ‚ AG(F,151P) [i] based on
  1. linear OA(128⁴⁴, 191, F₁₂₈, 41) (dual of [191, 147, 42]-code), using algebraic-geometric code AG(F,149P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (see above)
  2. linear OA(128⁴², 191, F₁₂₈, 39) (dual of [191, 149, 40]-code), using algebraic-geometric code AG(F,151P) [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.

None.

None.