MinT - Information on Result #1523267

Information on Result #1523267

Linear OOA(3¹³¹, 3234516, F₃, 3, 13) (dual of [(3234516, 3), 9703417, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³¹, 3234516, F₃, 2, 13) (dual of [(3234516, 2), 6468901, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³¹, 4194320, F₃, 2, 13) (dual of [(4194320, 2), 8388509, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 19, F₃, 2, 6) (dual of [(19, 2), 28, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 19)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹²¹, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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(3¹³¹, 1617257, F₃, 15, 13) (dual of [(1617257, 15), 24258724, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row