MinT - Information on Result #973544

Information on Result #973544

Linear OOA(5⁵⁸, 27, F₅, 3, 32) (dual of [(27, 3), 23, 33]-NRT-code), using OOA 2-folding based on linear OOA(5⁵⁸, 54, F₅, 2, 32) (dual of [(54, 2), 50, 33]-NRT-code), using

constructionÂ X applied to AG(2;F,67P) âŠ‚ AG(2;F,72P) [i] based on
1. linear OOA(5⁵⁴, 50, F₅, 2, 32) (dual of [(50, 2), 46, 33]-NRT-code), using algebraic-geometric NRT-code AG(2;F,67P) [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(5⁴⁹, 50, F₅, 2, 27) (dual of [(50, 2), 51, 28]-NRT-code), using algebraic-geometric NRT-code AG(2;F,72P) [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51 (see above)
3. linear OOA(5⁴, 4, F₅, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5⁴, 5, F₅, 2, 4) (dual of [(5, 2), 6, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;6,5) [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.