MinT - Information on Result #1048605

Information on Result #1048605

Linear OOA(8⁷⁸, 360, F₈, 3, 26) (dual of [(360, 3), 1002, 27]-NRT-code), using trace code based on linear OOA(64³⁹, 180, F₆₄, 3, 26) (dual of [(180, 3), 501, 27]-NRT-code), using

constructionÂ X applied to AG(3;F,501P) âŠ‚ AG(3;F,508P) [i] based on
1. linear OOA(64³³, 176, F₆₄, 3, 26) (dual of [(176, 3), 495, 27]-NRT-code), using algebraic-geometric NRT-code AG(3;F,501P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64²⁶, 176, F₆₄, 3, 19) (dual of [(176, 3), 502, 20]-NRT-code), using algebraic-geometric NRT-code AG(3;F,508P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64⁶, 4, F₆₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 3, 6) (dual of [(64, 3), 186, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;186,64) [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.