MinT - Information on Result #1117471

Information on Result #1117471

Linear OOA(3²¹², 4194347, F₃, 5, 13) (dual of [(4194347, 5), 20971523, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁶, 46, F₃, 5, 6) (dual of [(46, 5), 214, 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(3¹³, 42, F₃, 5, 6) (dual of [(42, 5), 197, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 13, 42)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁹⁶, 4194301, F₃, 5, 13) (dual of [(4194301, 5), 20971309, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁹⁶, 8388602, F₃, 3, 13) (dual of [(8388602, 3), 25165610, 14]-NRT-code), using
  - trace code [i] based on linear OOA(9⁹⁸, 4194301, F₉, 3, 13) (dual of [(4194301, 3), 12582805, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(9⁹⁸, 8388602, F₉, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁹, 4194301, F₈₁, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁹, 8388602, F₈₁, 13) (dual of [8388602, 8388553, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.