MinT - Information on Result #2498262

Information on Result #2498262

Linear OOA(4¹⁷⁶, 547, F₄, 2, 45) (dual of [(547, 2), 918, 46]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁷⁴, 546, F₄, 2, 45) (dual of [(546, 2), 918, 46]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁸, 182, F₆₄, 2, 45) (dual of [(182, 2), 306, 46]-NRT-code), using
- constructionÂ X applied to AG(2;F,306P) âŠ‚ AG(2;F,313P) [i] based on
  1. linear OOA(64⁵², 176, F₆₄, 2, 45) (dual of [(176, 2), 300, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,306P) [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, 2, 38) (dual of [(176, 2), 307, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,313P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁶, 6, F₆₄, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 2, 6) (dual of [(64, 2), 122, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;122,64) [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.