MinT - Information on Result #982333

Information on Result #982333

Linear OOA(8¹⁵⁴, 182, F₈, 3, 64) (dual of [(182, 3), 392, 65]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁵⁴, 364, F₈, 2, 64) (dual of [(364, 2), 574, 65]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁷, 182, F₆₄, 2, 64) (dual of [(182, 2), 287, 65]-NRT-code), using
- constructionÂ X applied to AG(2;F,287P) âŠ‚ AG(2;F,294P) [i] based on
  1. linear OOA(64⁷¹, 176, F₆₄, 2, 64) (dual of [(176, 2), 281, 65]-NRT-code), using algebraic-geometric NRT-code AG(2;F,287P) [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(64⁶⁴, 176, F₆₄, 2, 57) (dual of [(176, 2), 288, 58]-NRT-code), using algebraic-geometric NRT-code AG(2;F,294P) [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.