MinT - Information on Result #2451354

Information on Result #2451354

Linear OOA(8¹⁷³, 94, F₈, 2, 138) (dual of [(94, 2), 15, 139]-NRT-code), using strength reduction based on linear OOA(8¹⁷³, 94, F₈, 2, 139) (dual of [(94, 2), 15, 140]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(8⁴¹, 28, F₈, 2, 36) (dual of [(28, 2), 15, 37]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]
2. linear OOA(8¹¹⁷, 66, F₈, 2, 102) (dual of [(66, 2), 15, 103]-NRT-code), using
  - constructionÂ X applied to AG(2;F,25P) âŠ‚ AG(2;F,28P) [i] based on
    1. linear OOA(8¹¹⁵, 64, F₈, 2, 102) (dual of [(64, 2), 13, 103]-NRT-code), using algebraic-geometric NRT-code AG(2;F,25P) with known gap numbers [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(8¹¹³, 64, F₈, 2, 99) (dual of [(64, 2), 15, 100]-NRT-code), using algebraic-geometric NRT-code AG(2;F,28P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    3. linear OOA(8², 2, F₈, 2, 2) (dual of [(2, 2), 2, 3]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(8², 8, F₈, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;14,8) [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.