MinT - Information on Result #2643352

Information on Result #2643352

Linear OOA(8⁷⁴, 67, F₈, 3, 55) (dual of [(67, 3), 127, 56]-NRT-code), using strength reduction based on linear OOA(8⁷⁴, 67, F₈, 3, 56) (dual of [(67, 3), 127, 57]-NRT-code), using

constructionÂ X applied to AG(3;F,135P) âŠ‚ AG(3;F,140P) [i] based on
1. linear OOA(8⁷⁰, 64, F₈, 3, 56) (dual of [(64, 3), 122, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,135P) [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(8⁶⁵, 64, F₈, 3, 51) (dual of [(64, 3), 127, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,140P) [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]

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.