MinT - Information on Result #2489813

Information on Result #2489813

Linear OOA(3²¹⁴, 294, F₃, 2, 57) (dual of [(294, 2), 374, 58]-NRT-code), using 3¹ times duplication based on linear OOA(3²¹³, 294, F₃, 2, 57) (dual of [(294, 2), 375, 58]-NRT-code), using

trace code [i] based on linear OOA(27⁷¹, 98, F₂₇, 2, 57) (dual of [(98, 2), 125, 58]-NRT-code), using
- constructionÂ X applied to AG(2;F,132P) âŠ‚ AG(2;F,136P) [i] based on
  1. linear OOA(27⁶⁸, 95, F₂₇, 2, 57) (dual of [(95, 2), 122, 58]-NRT-code), using algebraic-geometric NRT-code AG(2;F,132P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(27⁶⁴, 95, F₂₇, 2, 53) (dual of [(95, 2), 126, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,136P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96 (see above)
  3. linear OOA(27³, 3, F₂₇, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27³, 27, F₂₇, 2, 3) (dual of [(27, 2), 51, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;51,27) [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.