MinT - Information on Result #961705

Information on Result #961705

Linear OOA(4¹⁸², 4194301, F₄, 3, 17) (dual of [(4194301, 3), 12582721, 18]-NRT-code), using OOA 2-folding based on linear OOA(4¹⁸², 8388602, F₄, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), using

trace code [i] based on linear OOA(16⁹¹, 4194301, F₁₆, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁹¹, 8388602, F₁₆, 17) (dual of [8388602, 8388511, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹¹, large, F₁₆, 17) (dual of [large, large−91, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 16⁶âˆ’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(4¹⁸², 4194301, F₄, 3, 16) (dual of [(4194301, 3), 12582721, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4¹⁸⁵, 4194302, F₄, 3, 17) (dual of [(4194302, 3), 12582721, 18]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4¹⁸⁸, 4194303, F₄, 3, 17) (dual of [(4194303, 3), 12582721, 18]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
4	Linear OOA(4¹⁸³, 4194301, F₄, 3, 17) (dual of [(4194301, 3), 12582720, 18]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(4¹⁸⁴, 4194301, F₄, 3, 17) (dual of [(4194301, 3), 12582719, 18]-NRT-code)	[i]	OOA Duplication
6	Linear OOA(4¹⁹⁰, 4194306, F₄, 3, 17) (dual of [(4194306, 3), 12582728, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(4¹⁹¹, 4194310, F₄, 3, 17) (dual of [(4194310, 3), 12582739, 18]-NRT-code)	[i]
8	Linear OOA(4¹⁹², 4194311, F₄, 3, 17) (dual of [(4194311, 3), 12582741, 18]-NRT-code)	[i]
9	Linear OOA(4¹⁹³, 4194315, F₄, 3, 17) (dual of [(4194315, 3), 12582752, 18]-NRT-code)	[i]
10	Linear OOA(4¹⁹⁴, 4194318, F₄, 3, 17) (dual of [(4194318, 3), 12582760, 18]-NRT-code)	[i]