MinT - Information on Result #2490566

Information on Result #2490566

Linear OOA(3²⁴⁵, 295, F₃, 2, 67) (dual of [(295, 2), 345, 68]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²⁴³, 294, F₃, 2, 67) (dual of [(294, 2), 345, 68]-NRT-code), using

trace code [i] based on linear OOA(27⁸¹, 98, F₂₇, 2, 67) (dual of [(98, 2), 115, 68]-NRT-code), using
- constructionÂ X applied to AG(2;F,122P) âŠ‚ AG(2;F,126P) [i] based on
  1. linear OOA(27⁷⁸, 95, F₂₇, 2, 67) (dual of [(95, 2), 112, 68]-NRT-code), using algebraic-geometric NRT-code AG(2;F,122P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(27⁷⁴, 95, F₂₇, 2, 63) (dual of [(95, 2), 116, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,126P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96 (see above)
  3. linear OOA(27³, 3, F₂₇, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27³, 27, F₂₇, 2, 3) (dual of [(27, 2), 51, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;51,27) [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.