MinT - Information on Result #1049352

Information on Result #1049352

Linear OOA(8¹⁶⁸, 135, F₈, 3, 87) (dual of [(135, 3), 237, 88]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶¹, 67, F₈, 3, 43) (dual of [(67, 3), 140, 44]-NRT-code), using
- constructionÂ X applied to AG(3;F,148P) âŠ‚ AG(3;F,153P) [i] based on
  1. linear OOA(8⁵⁷, 64, F₈, 3, 43) (dual of [(64, 3), 135, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,148P) [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, 3, 38) (dual of [(64, 3), 140, 39]-NRT-code), using algebraic-geometric NRT-code AG(3;F,153P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;20,8) [i]
linear OOA(8¹⁰⁷, 68, F₈, 3, 87) (dual of [(68, 3), 97, 88]-NRT-code), using
- constructionÂ X applied to AG(3;F,104P) âŠ‚ AG(3;F,111P) [i] based on
  1. linear OOA(8¹⁰¹, 64, F₈, 3, 87) (dual of [(64, 3), 91, 88]-NRT-code), using algebraic-geometric NRT-code AG(3;F,104P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹⁴, 64, F₈, 3, 80) (dual of [(64, 3), 98, 81]-NRT-code), using algebraic-geometric NRT-code AG(3;F,111P) [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]

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.