MinT - Information on Result #1184476

Information on Result #1184476

Digital (231, 248, 2097153)-net over F₃, using net defined by OOA based on linear OOA(3²⁴⁸, 2097153, F₃, 20, 17) (dual of [(2097153, 20), 41942812, 18]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3²⁴⁸, 4194307, F₃, 4, 17) (dual of [(4194307, 4), 16776980, 18]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁷⁶, 2097150, F₃, 4, 8) (dual of [(2097150, 4), 8388524, 9]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  3. linear OOA(3¹⁶⁶, 2097150, F₃, 4, 17) (dual of [(2097150, 4), 8388434, 18]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3¹⁶⁶, 8388600, F₃, 17) (dual of [8388600, 8388434, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.