MinT - Information on Result #1531238

Information on Result #1531238

Linear OOA(3²³⁰, 4174786, F₃, 3, 21) (dual of [(4174786, 3), 12524128, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁰, 4174786, F₃, 2, 21) (dual of [(4174786, 2), 8349342, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁰, 4194324, F₃, 2, 21) (dual of [(4194324, 2), 8388418, 22]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁰, 23, F₃, 2, 10) (dual of [(23, 2), 26, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (10, 20, 23)-net over F₃, using
      - 3 times m-reduction [i] based on digital (10, 23, 23)-net over F₃, using
        a shift-net [i]
  2. linear OOA(3²¹⁰, 4194301, F₃, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3²¹⁰, 8388602, F₃, 21) (dual of [8388602, 8388392, 22]-code), using
      - discarding factors / shortening the dual code based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(3²³⁰, 2087393, F₃, 5, 21) (dual of [(2087393, 5), 10436735, 22]-NRT-code)	[i]		OOA Folding