MinT - Information on Result #1049291

Information on Result #1049291

Linear OOA(8¹⁶⁴, 137, F₈, 3, 82) (dual of [(137, 3), 247, 83]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶¹, 68, F₈, 3, 41) (dual of [(68, 3), 143, 42]-NRT-code), using
- constructionÂ X applied to AG(3;F,150P) âŠ‚ AG(3;F,157P) [i] based on
  1. linear OOA(8⁵⁵, 64, F₈, 3, 41) (dual of [(64, 3), 137, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,150P) [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(8⁴⁸, 64, F₈, 3, 34) (dual of [(64, 3), 144, 35]-NRT-code), using algebraic-geometric NRT-code AG(3;F,157P) [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(8¹⁰³, 69, F₈, 3, 82) (dual of [(69, 3), 104, 83]-NRT-code), using
- constructionÂ X applied to AG(3;F,109P) âŠ‚ AG(3;F,117P) [i] based on
  1. linear OOA(8⁹⁶, 64, F₈, 3, 82) (dual of [(64, 3), 96, 83]-NRT-code), using algebraic-geometric NRT-code AG(3;F,109P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸⁸, 64, F₈, 3, 74) (dual of [(64, 3), 104, 75]-NRT-code), using algebraic-geometric NRT-code AG(3;F,117P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁷, 5, F₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 3, 7) (dual of [(8, 3), 17, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;17,8) [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.