MinT - Information on Result #1650848

Information on Result #1650848

Linear OOA(3²³¹, 4194326, F₃, 5, 21) (dual of [(4194326, 5), 20971399, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³¹, 4194326, F₃, 2, 21) (dual of [(4194326, 2), 8388421, 22]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²¹, 25, F₃, 2, 10) (dual of [(25, 2), 29, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (11, 21, 25)-net over F₃, using
    - 4 times m-reduction [i] based on digital (11, 25, 25)-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(3²³¹, 2097162, F₃, 25, 21) (dual of [(2097162, 25), 52428819, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row