MinT - Information on Result #1084653

Information on Result #1084653

Linear OOA(3²¹⁹, 4194318, F₃, 4, 15) (dual of [(4194318, 4), 16777053, 16]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁸, 18, F₃, 4, 5) (dual of [(18, 4), 64, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 8, 18)-net over F₃, using
  - linear code embedding found in a computer search [i]
linear OOA(3⁶¹, 2097150, F₃, 4, 7) (dual of [(2097150, 4), 8388539, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁶¹, 2796200, F₃, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OA(3⁶¹, 8388601, F₃, 7) (dual of [8388601, 8388540, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(3¹⁵⁰, 2097150, F₃, 4, 15) (dual of [(2097150, 4), 8388450, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁵⁰, 8388600, F₃, 15) (dual of [8388600, 8388450, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁹, 2097158, F₃, 20, 15) (dual of [(2097158, 20), 41942941, 16]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row