MinT - Information on Result #941434

Information on Result #941434

Linear OOA(8¹⁶⁷, 137, F₈, 2, 87) (dual of [(137, 2), 107, 88]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶¹, 68, F₈, 2, 43) (dual of [(68, 2), 75, 44]-NRT-code), using
- constructionÂ X applied to AG(2;F,84P) âŠ‚ AG(2;F,89P) [i] based on
  1. linear OOA(8⁵⁷, 64, F₈, 2, 43) (dual of [(64, 2), 71, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,84P) [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(8⁵², 64, F₈, 2, 38) (dual of [(64, 2), 76, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,89P) [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]
linear OOA(8¹⁰⁶, 69, F₈, 2, 87) (dual of [(69, 2), 32, 88]-NRT-code), using
- constructionÂ X applied to AG(2;F,40P) âŠ‚ AG(2;F,46P) [i] based on
  1. linear OOA(8¹⁰¹, 64, F₈, 2, 87) (dual of [(64, 2), 27, 88]-NRT-code), using algebraic-geometric NRT-code AG(2;F,40P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹⁵, 64, F₈, 2, 81) (dual of [(64, 2), 33, 82]-NRT-code), using algebraic-geometric NRT-code AG(2;F,46P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁵, 5, F₈, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁵, 8, F₈, 2, 5) (dual of [(8, 2), 11, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;11,8) [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.