MinT - Information on Result #2486272

Information on Result #2486272

Linear OOA(3¹⁸², 4194324, F₃, 2, 17) (dual of [(4194324, 2), 8388466, 18]-NRT-code), using 1 times NRT-code embedding in larger space 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: Constructive and 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		Method
1	Linear OOA(3¹⁸³, 4194324, F₃, 2, 17) (dual of [(4194324, 2), 8388465, 18]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁸², 4119481, F₃, 3, 17) (dual of [(4119481, 3), 12358261, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3¹⁸², 4119481, F₃, 4, 17) (dual of [(4119481, 4), 16477742, 18]-NRT-code)	[i]
4	Linear OOA(3¹⁸², 4119481, F₃, 5, 17) (dual of [(4119481, 5), 20597223, 18]-NRT-code)	[i]
5	Digital (165, 182, 4119481)-net over F₃	[i]
6	Linear OOA(3¹⁸², 2097162, F₃, 4, 17) (dual of [(2097162, 4), 8388466, 18]-NRT-code)	[i]	OOA Folding