MinT - Information on Result #1049328

Information on Result #1049328

Linear OOA(8¹⁶⁷, 136, F₈, 3, 85) (dual of [(136, 3), 241, 86]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶², 68, F₈, 3, 42) (dual of [(68, 3), 142, 43]-NRT-code), using
- constructionÂ X applied to AG(3;F,149P) âŠ‚ AG(3;F,156P) [i] based on
  1. linear OOA(8⁵⁶, 64, F₈, 3, 42) (dual of [(64, 3), 136, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,149P) [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(8⁴⁹, 64, F₈, 3, 35) (dual of [(64, 3), 143, 36]-NRT-code), using algebraic-geometric NRT-code AG(3;F,156P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁶, 4, F₈, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁶, 8, F₈, 3, 6) (dual of [(8, 3), 18, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;18,8) [i]
linear OOA(8¹⁰⁵, 68, F₈, 3, 85) (dual of [(68, 3), 99, 86]-NRT-code), using
- constructionÂ X applied to AG(3;F,106P) âŠ‚ AG(3;F,113P) [i] based on
  1. linear OOA(8⁹⁹, 64, F₈, 3, 85) (dual of [(64, 3), 93, 86]-NRT-code), using algebraic-geometric NRT-code AG(3;F,106P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹², 64, F₈, 3, 78) (dual of [(64, 3), 100, 79]-NRT-code), using algebraic-geometric NRT-code AG(3;F,113P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁶, 4, F₈, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code) (see above)

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.