MinT - Information on Result #2514197

Information on Result #2514197

Linear OOA(9¹³⁵, 744, F₉, 2, 48) (dual of [(744, 2), 1353, 49]-NRT-code), using 9¹ times duplication based on linear OOA(9¹³⁴, 744, F₉, 2, 48) (dual of [(744, 2), 1354, 49]-NRT-code), using

trace code [i] based on linear OOA(81⁶⁷, 372, F₈₁, 2, 48) (dual of [(372, 2), 677, 49]-NRT-code), using
- constructionÂ X applied to AG(2;F,689P) âŠ‚ AG(2;F,693P) [i] based on
  1. linear OOA(81⁶⁴, 369, F₈₁, 2, 48) (dual of [(369, 2), 674, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,689P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(81⁶⁰, 369, F₈₁, 2, 44) (dual of [(369, 2), 678, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,693P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81³, 3, F₈₁, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81³, 81, F₈₁, 2, 3) (dual of [(81, 2), 159, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;159,81) [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.