MinT - Information on Result #2623691

Information on Result #2623691

Linear OOA(3¹⁵⁹, 58, F₃, 3, 110) (dual of [(58, 3), 15, 111]-NRT-code), using strength reduction based on linear OOA(3¹⁵⁹, 58, F₃, 3, 111) (dual of [(58, 3), 15, 112]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁶⁹, 28, F₃, 3, 54) (dual of [(28, 3), 15, 55]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,29P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁷⁵, 30, F₃, 3, 56) (dual of [(30, 3), 15, 57]-NRT-code), using
  - constructionÂ X applied to AG(3;F,24P) âŠ‚ AG(3;F,29P) [i] based on
    1. linear OOA(3⁷¹, 27, F₃, 3, 56) (dual of [(27, 3), 10, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,24P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
    2. linear OOA(3⁶⁶, 27, F₃, 3, 51) (dual of [(27, 3), 15, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,29P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
    3. linear OOA(3⁴, 3, F₃, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;5,3) [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.