MinT - Information on Result #1526360

Information on Result #1526360

Linear OOA(3¹⁸⁰, 3521130, F₃, 3, 17) (dual of [(3521130, 3), 10563210, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁰, 3521130, F₃, 2, 17) (dual of [(3521130, 2), 7042080, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁰, 4194323, F₃, 2, 17) (dual of [(4194323, 2), 8388466, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁴, 22, F₃, 2, 8) (dual of [(22, 2), 30, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 14, 22)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(3¹⁸⁰, 1760565, F₃, 5, 17) (dual of [(1760565, 5), 8802645, 18]-NRT-code)	[i]		OOA Folding