MinT - Information on Result #671086

Information on Result #671086

Linear OA(128⁵⁴, 388, F₁₂₈, 31) (dual of [388, 334, 32]-code), using (u,Â u+v)-construction based on

linear OA(128¹⁹, 194, F₁₂₈, 15) (dual of [194, 175, 16]-code), using
- constructionÂ X applied to AG(F,175P) âŠ‚ AG(F,177P) [i] based on
  1. linear OA(128¹⁸, 191, F₁₂₈, 15) (dual of [191, 173, 16]-code), using algebraic-geometric code AG(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]
  2. linear OA(128¹⁶, 191, F₁₂₈, 13) (dual of [191, 175, 14]-code), using algebraic-geometric code AG(F,177P) [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(128³⁵, 194, F₁₂₈, 31) (dual of [194, 159, 32]-code), using
- constructionÂ X applied to AG(F,159P) âŠ‚ AG(F,161P) [i] based on
  1. linear OA(128³⁴, 191, F₁₂₈, 31) (dual of [191, 157, 32]-code), using algebraic-geometric code AG(F,159P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (see above)
  2. 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)
  3. linear OA(128¹, 3, F₁₂₈, 1) (dual of [3, 2, 2]-code) (see above)

Mode: Constructive and linear.

None.

None.