MinT - Information on Result #1016385

Information on Result #1016385

Linear OOA(9⁹⁹, 19712, F₉, 3, 20) (dual of [(19712, 3), 59037, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹³, 28, F₉, 3, 10) (dual of [(28, 3), 71, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,73P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9⁸⁶, 19684, F₉, 3, 20) (dual of [(19684, 3), 58966, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9⁸⁶, 59052, F₉, 20) (dual of [59052, 58966, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁸⁶, 59054, F₉, 20) (dual of [59054, 58968, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(9⁸⁶, 59049, F₉, 20) (dual of [59049, 58963, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(9⁸¹, 59049, F₉, 19) (dual of [59049, 58968, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.