MinT - Information on Result #2710149

Information on Result #2710149

OOA(9¹¹⁵, 5598964, S₉, 3, 12), using 9¹ times duplication based on OOA(9¹¹⁴, 5598964, S₉, 3, 12), using

(u,Â u+v)-construction [i] based on
1. OOA(9²⁴, 6562, S₉, 3, 6), using
  - OOA 3-folding [i] based on OA(9²⁴, 19686, S₉, 6), using
    - discarding parts of the base [i] based on linear OA(27¹⁶, 19686, F₂₇, 6) (dual of [19686, 19670, 7]-code), using
      - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(27¹⁶, 19683, F₂₇, 6) (dual of [19683, 19667, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(27¹³, 19683, F₂₇, 5) (dual of [19683, 19670, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. linear OOA(9⁹⁰, 5592402, F₉, 3, 12) (dual of [(5592402, 3), 16777116, 13]-NRT-code), using
  - trace code [i] based on linear OOA(81⁴⁵, 2796201, F₈₁, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive.

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.