MinT - Information on Result #990866

Information on Result #990866

Linear OOA(64⁷⁸, 90, F₆₄, 3, 67) (dual of [(90, 3), 192, 68]-NRT-code), using OOA 2-folding based on linear OOA(64⁷⁸, 180, F₆₄, 2, 67) (dual of [(180, 2), 282, 68]-NRT-code), using

constructionÂ X applied to AG(2;F,284P) âŠ‚ AG(2;F,289P) [i] based on
1. linear OOA(64⁷⁴, 176, F₆₄, 2, 67) (dual of [(176, 2), 278, 68]-NRT-code), using algebraic-geometric NRT-code AG(2;F,284P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64⁶⁹, 176, F₆₄, 2, 62) (dual of [(176, 2), 283, 63]-NRT-code), using algebraic-geometric NRT-code AG(2;F,289P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;124,64) [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.