MinT - Information on Result #1129611

Information on Result #1129611

Linear OOA(3²¹⁵, 77, F₃, 5, 101) (dual of [(77, 5), 170, 102]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁸¹, 38, F₃, 5, 50) (dual of [(38, 5), 109, 51]-NRT-code), using
- constructionÂ X applied to AG(5;F,64P) âŠ‚ AG(5;F,67P) [i] based on
  1. linear OOA(3⁷⁷, 36, F₃, 5, 51) (dual of [(36, 5), 103, 52]-NRT-code), using algebraic-geometric NRT-code AG(5;F,64P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁷¹, 36, F₃, 5, 45) (dual of [(36, 5), 109, 46]-NRT-code), using algebraic-geometric NRT-code AG(5;F,67P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3⁴, 2, F₃, 5, 4) (dual of [(2, 5), 6, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁴, 3, F₃, 5, 4) (dual of [(3, 5), 11, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(5;11,3) [i]
linear OOA(3¹³⁴, 39, F₃, 5, 101) (dual of [(39, 5), 61, 102]-NRT-code), using
- constructionÂ X applied to AG(5;F,39P) âŠ‚ AG(5;F,43P) [i] based on
  1. linear OOA(3¹²⁷, 36, F₃, 5, 101) (dual of [(36, 5), 53, 102]-NRT-code), using algebraic-geometric NRT-code AG(5;F,39P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  2. linear OOA(3¹¹⁹, 36, F₃, 5, 93) (dual of [(36, 5), 61, 94]-NRT-code), using algebraic-geometric NRT-code AG(5;F,43P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3⁷, 3, F₃, 5, 7) (dual of [(3, 5), 8, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(5;8,3) [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.