MinT - Information on Result #2514692

Information on Result #2514692

Linear OOA(9¹⁴⁹, 348, F₉, 2, 64) (dual of [(348, 2), 547, 65]-NRT-code), using 9¹ times duplication based on linear OOA(9¹⁴⁸, 348, F₉, 2, 64) (dual of [(348, 2), 548, 65]-NRT-code), using

trace code [i] based on linear OOA(81⁷⁴, 174, F₈₁, 2, 64) (dual of [(174, 2), 274, 65]-NRT-code), using
- constructionÂ X applied to AG(2;F,277P) âŠ‚ AG(2;F,281P) [i] based on
  1. linear OOA(81⁷¹, 171, F₈₁, 2, 64) (dual of [(171, 2), 271, 65]-NRT-code), using algebraic-geometric NRT-code AG(2;F,277P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(81⁶⁷, 171, F₈₁, 2, 60) (dual of [(171, 2), 275, 61]-NRT-code), using algebraic-geometric NRT-code AG(2;F,281P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (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.