MinT - Information on Result #982286

Information on Result #982286

Linear OOA(8¹²⁷, 67, F₈, 3, 63) (dual of [(67, 3), 74, 64]-NRT-code), using OOA 2-folding based on linear OOA(8¹²⁷, 134, F₈, 2, 63) (dual of [(134, 2), 141, 64]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8⁴⁵, 65, F₈, 2, 31) (dual of [(65, 2), 85, 32]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,98P) [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(8⁸², 69, F₈, 2, 63) (dual of [(69, 2), 56, 64]-NRT-code), using
  - constructionÂ X applied to AG(2;F,64P) âŠ‚ AG(2;F,70P) [i] based on
    1. linear OOA(8⁷⁷, 64, F₈, 2, 63) (dual of [(64, 2), 51, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,64P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    2. linear OOA(8⁷¹, 64, F₈, 2, 57) (dual of [(64, 2), 57, 58]-NRT-code), using algebraic-geometric NRT-code AG(2;F,70P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    3. linear OOA(8⁵, 5, F₈, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(8⁵, 8, F₈, 2, 5) (dual of [(8, 2), 11, 6]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;11,8) [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.