MinT - Information on Result #1440927

Information on Result #1440927

Linear OOA(7⁴³, 179, F₇, 2, 18) (dual of [(179, 2), 315, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(7⁴³, 179, F₇, 18) (dual of [179, 136, 19]-code), using

discarding factors / shortening the dual code based on linear OA(7⁴³, 186, F₇, 18) (dual of [186, 143, 19]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁴², 184, F₇, 18) (dual of [184, 142, 19]-code), using
    - trace code [i] based on linear OA(49²¹, 92, F₄₉, 18) (dual of [92, 71, 19]-code), using
      - extended algebraic-geometric code AG_e(F,73P) [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
        a curve from the manYPoints database [i]
  2. linear OA(7⁴², 185, F₇, 17) (dual of [185, 143, 18]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁴²Â > V_b^sâˆ’1(kâˆ’1)Â = 120849 312361 766561 336729 476435 442497 [i]
  3. linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

Mode: 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.