MinT - Information on Result #1613090

Information on Result #1613090

Linear OOA(3²⁴⁹, 3241315, F₃, 4, 23) (dual of [(3241315, 4), 12965011, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁹, 3241315, F₃, 2, 23) (dual of [(3241315, 2), 6482381, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴⁹, 4194327, F₃, 2, 23) (dual of [(4194327, 2), 8388405, 24]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²³, 26, F₃, 2, 11) (dual of [(26, 2), 29, 12]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 23, 26)-net over F₃, using
      - 3 times m-reduction [i] based on digital (12, 26, 26)-net over F₃, using
        a shift-net [i]
  2. linear OOA(3²²⁶, 4194301, F₃, 2, 23) (dual of [(4194301, 2), 8388376, 24]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3²²⁶, 8388602, F₃, 23) (dual of [8388602, 8388376, 24]-code), using
      - discarding factors / shortening the dual code based on linear OA(3²²⁶, large, F₃, 23) (dual of [large, large−226, 24]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [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(3²⁴⁹, 1080438, F₃, 28, 23) (dual of [(1080438, 28), 30252015, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row