MinT - Information on Result #1117360

Information on Result #1117360

Linear OOA(3²⁰⁷, 4194665, F₃, 5, 12) (dual of [(4194665, 5), 20973118, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁷, 364, F₃, 5, 6) (dual of [(364, 5), 1793, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3²⁷, 1092, F₃, 6) (dual of [1092, 1065, 7]-code), using
  - 1 times truncation [i] based on linear OA(3²⁸, 1093, F₃, 7) (dual of [1093, 1065, 8]-code), using
    - the BCH-code C(I) with length 1093Â | 3⁷âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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.