MinT - Information on Result #1015940

Information on Result #1015940

Linear OOA(9⁷⁴, 5621929, F₉, 3, 8) (dual of [(5621929, 3), 16865713, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁶, 29527, F₉, 3, 4) (dual of [(29527, 3), 88565, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(9¹⁶, 59054, F₉, 4) (dual of [59054, 59038, 5]-code), using
  - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
    1. linear OA(9¹⁶, 59049, F₉, 4) (dual of [59049, 59033, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    2. linear OA(9¹¹, 59049, F₉, 3) (dual of [59049, 59038, 4]-code or 59049-cap in PG(10,9)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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]
linear OOA(9⁵⁸, 5592402, F₉, 3, 8) (dual of [(5592402, 3), 16777148, 9]-NRT-code), using
- trace code [i] based on linear OOA(81²⁹, 2796201, F₈₁, 3, 8) (dual of [(2796201, 3), 8388574, 9]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(81²⁹, large, F₈₁, 8) (dual of [large, large−29, 9]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.