MinT - Information on Result #1117371

Information on Result #1117371

Linear OOA(3²⁴³, 6990506, F₃, 5, 12) (dual of [(6990506, 5), 34952287, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶³, 2796205, F₃, 5, 6) (dual of [(2796205, 5), 13980962, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3³, 4, F₃, 5, 3) (dual of [(4, 5), 17, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;17,3) [i]
  2. linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(3¹⁸⁰, 4194301, F₃, 5, 12) (dual of [(4194301, 5), 20971325, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁸⁰, 8388602, F₃, 3, 12) (dual of [(8388602, 3), 25165626, 13]-NRT-code), using
  - trace code [i] based on linear OOA(9⁹⁰, 4194301, F₉, 3, 12) (dual of [(4194301, 3), 12582813, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(9⁹⁰, 8388602, F₉, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁵, 4194301, F₈₁, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁵, 8388602, F₈₁, 12) (dual of [8388602, 8388557, 13]-code), using
        discarding factors / shortening the dual code 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 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.