MinT - Information on Result #2623631

Information on Result #2623631

Linear OOA(3¹⁵⁸, 58, F₃, 3, 106) (dual of [(58, 3), 16, 107]-NRT-code), using strength reduction based on linear OOA(3¹⁵⁸, 58, F₃, 3, 109) (dual of [(58, 3), 16, 110]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁶⁸, 28, F₃, 3, 53) (dual of [(28, 3), 16, 54]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,30P) [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(3⁷⁴, 30, F₃, 3, 55) (dual of [(30, 3), 16, 56]-NRT-code), using
  - constructionÂ X applied to AG(3;F,25P) âŠ‚ AG(3;F,30P) [i] based on
    1. linear OOA(3⁷⁰, 27, F₃, 3, 55) (dual of [(27, 3), 11, 56]-NRT-code), using algebraic-geometric NRT-code AG(3;F,25P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
    2. linear OOA(3⁶⁵, 27, F₃, 3, 50) (dual of [(27, 3), 16, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,30P) [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.