MinT - Information on Result #1182993

Information on Result #1182993

Linear OOA(3¹⁰⁶, 4194303, F₃, 12, 8) (dual of [(4194303, 12), 50331530, 9]-NRT-code), using OOA stacking with additional row based on linear OOA(3¹⁰⁶, 4194304, F₃, 4, 8) (dual of [(4194304, 4), 16777110, 9]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3², 4, F₃, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;14,3) [i]
2. linear OOA(3²⁸, 2097150, F₃, 4, 4) (dual of [(2097150, 4), 8388572, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3²⁸, 2391484, F₃, 4, 4) (dual of [(2391484, 4), 9565908, 5]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(3²⁸, 2391485, F₃, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F₃, using
        nets constructed from net-embeddable BCH codes [i]
3. 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]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (98, 106, 4194303)-net over F₃	[i]		Net Defined by OOA