MinT - Information on Result #2648637

Information on Result #2648637

Linear OOA(64⁵⁴, 179, F₆₄, 3, 42) (dual of [(179, 3), 483, 43]-NRT-code), using strength reduction based on linear OOA(64⁵⁴, 179, F₆₄, 3, 43) (dual of [(179, 3), 483, 44]-NRT-code), using

constructionÂ X applied to AG(3;F,484P) âŠ‚ AG(3;F,489P) [i] based on
1. linear OOA(64⁵⁰, 176, F₆₄, 3, 43) (dual of [(176, 3), 478, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,484P) [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(64⁴⁵, 176, F₆₄, 3, 38) (dual of [(176, 3), 483, 39]-NRT-code), using algebraic-geometric NRT-code AG(3;F,489P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;188,64) [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.