MinT - Information on Result #1016230

Information on Result #1016230

Linear OOA(9¹⁰², 1594353, F₉, 3, 15) (dual of [(1594353, 3), 4782957, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁰, 28, F₉, 3, 7) (dual of [(28, 3), 74, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,76P) [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(9⁹², 1594325, F₉, 3, 15) (dual of [(1594325, 3), 4782883, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9⁹², 4782975, F₉, 15) (dual of [4782975, 4782883, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁹², 4782976, F₉, 15) (dual of [4782976, 4782884, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
      1. linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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.