MinT - Information on Result #941131

Information on Result #941131

Linear OOA(8¹³⁷, 135, F₈, 2, 68) (dual of [(135, 2), 133, 69]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵¹, 67, F₈, 2, 34) (dual of [(67, 2), 83, 35]-NRT-code), using
- constructionÂ X applied to AG(2;F,93P) âŠ‚ AG(2;F,97P) [i] based on
  1. linear OOA(8⁴⁸, 64, F₈, 2, 34) (dual of [(64, 2), 80, 35]-NRT-code), using algebraic-geometric NRT-code AG(2;F,93P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]
  2. linear OOA(8⁴⁴, 64, F₈, 2, 30) (dual of [(64, 2), 84, 31]-NRT-code), using algebraic-geometric NRT-code AG(2;F,97P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8³, 3, F₈, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8³, 8, F₈, 2, 3) (dual of [(8, 2), 13, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;13,8) [i]
linear OOA(8⁸⁶, 68, F₈, 2, 68) (dual of [(68, 2), 50, 69]-NRT-code), using
- constructionÂ X applied to AG(2;F,59P) âŠ‚ AG(2;F,64P) [i] based on
  1. linear OOA(8⁸², 64, F₈, 2, 68) (dual of [(64, 2), 46, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,59P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁷⁷, 64, F₈, 2, 63) (dual of [(64, 2), 51, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,64P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁴, 4, F₈, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 2, 4) (dual of [(8, 2), 12, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;12,8) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.