MinT - Information on Result #961963

Information on Result #961963

Linear OOA(4²¹⁸, 4194301, F₄, 3, 20) (dual of [(4194301, 3), 12582685, 21]-NRT-code), using OOA 2-folding based on linear OOA(4²¹⁸, 8388602, F₄, 2, 20) (dual of [(8388602, 2), 16776986, 21]-NRT-code), using

trace code [i] based on linear OOA(16¹⁰⁹, 4194301, F₁₆, 2, 20) (dual of [(4194301, 2), 8388493, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16¹⁰⁹, 8388602, F₁₆, 20) (dual of [8388602, 8388493, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁰⁹, large, F₁₆, 20) (dual of [large, large−109, 21]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 16⁶âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(4²²¹, 4194302, F₄, 3, 20) (dual of [(4194302, 3), 12582685, 21]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4²²⁴, 4194303, F₄, 3, 20) (dual of [(4194303, 3), 12582685, 21]-NRT-code)	[i]
3	Linear OOA(4²²⁷, 4194304, F₄, 3, 20) (dual of [(4194304, 3), 12582685, 21]-NRT-code)	[i]
4	Linear OOA(4²¹⁹, 4194301, F₄, 3, 20) (dual of [(4194301, 3), 12582684, 21]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(4²²⁰, 4194301, F₄, 3, 20) (dual of [(4194301, 3), 12582683, 21]-NRT-code)	[i]	OOA Duplication
6	Linear OOA(4²²⁸, 4194306, F₄, 3, 20) (dual of [(4194306, 3), 12582690, 21]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(4²²⁹, 4194310, F₄, 3, 20) (dual of [(4194310, 3), 12582701, 21]-NRT-code)	[i]
8	Linear OOA(4²³⁰, 4194311, F₄, 3, 20) (dual of [(4194311, 3), 12582703, 21]-NRT-code)	[i]