MinT - Information on Result #1529606

Information on Result #1529606

Linear OOA(3²¹⁵, 3411629, F₃, 3, 20) (dual of [(3411629, 3), 10234672, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁵, 3411629, F₃, 2, 20) (dual of [(3411629, 2), 6823043, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁵, 4194322, F₃, 2, 20) (dual of [(4194322, 2), 8388429, 21]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁹, 21, F₃, 2, 10) (dual of [(21, 2), 23, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 19, 21)-net over F₃, using
      - 2 times m-reduction [i] based on digital (9, 21, 21)-net over F₃, using
        a shift-net [i]
  2. linear OOA(3¹⁹⁶, 4194301, F₃, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁹⁶, 8388602, F₃, 20) (dual of [8388602, 8388406, 21]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁵, 1705814, F₃, 5, 20) (dual of [(1705814, 5), 8528855, 21]-NRT-code)	[i]		OOA Folding