MinT - Information on Result #961780

Information on Result #961780

Linear OOA(4¹⁹⁴, 4194301, F₄, 3, 18) (dual of [(4194301, 3), 12582709, 19]-NRT-code), using OOA 2-folding based on linear OOA(4¹⁹⁴, 8388602, F₄, 2, 18) (dual of [(8388602, 2), 16777010, 19]-NRT-code), using

trace code [i] based on linear OOA(16⁹⁷, 4194301, F₁₆, 2, 18) (dual of [(4194301, 2), 8388505, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁹⁷, 8388602, F₁₆, 18) (dual of [8388602, 8388505, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹⁷, large, F₁₆, 18) (dual of [large, large−97, 19]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 16⁶âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(4¹⁹⁷, 4194302, F₄, 3, 18) (dual of [(4194302, 3), 12582709, 19]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4²⁰⁰, 4194303, F₄, 3, 18) (dual of [(4194303, 3), 12582709, 19]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4¹⁹⁵, 4194301, F₄, 3, 18) (dual of [(4194301, 3), 12582708, 19]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(4¹⁹⁶, 4194301, F₄, 3, 18) (dual of [(4194301, 3), 12582707, 19]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(4²⁰³, 4194306, F₄, 3, 18) (dual of [(4194306, 3), 12582715, 19]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
6	Linear OOA(4²⁰⁴, 4194310, F₄, 3, 18) (dual of [(4194310, 3), 12582726, 19]-NRT-code)	[i]
7	Linear OOA(4²⁰⁵, 4194311, F₄, 3, 18) (dual of [(4194311, 3), 12582728, 19]-NRT-code)	[i]
8	Linear OOA(4²⁰⁶, 4194315, F₄, 3, 18) (dual of [(4194315, 3), 12582739, 19]-NRT-code)	[i]