MinT - Information on Result #972137

Information on Result #972137

Linear OOA(5¹⁰², 4194301, F₅, 3, 11) (dual of [(4194301, 3), 12582801, 12]-NRT-code), using OOA 2-folding based on linear OOA(5¹⁰², 8388602, F₅, 2, 11) (dual of [(8388602, 2), 16777102, 12]-NRT-code), using

trace code [i] based on linear OOA(25⁵¹, 4194301, F₂₅, 2, 11) (dual of [(4194301, 2), 8388551, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵¹, 8388602, F₂₅, 11) (dual of [8388602, 8388551, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵¹, large, F₂₅, 11) (dual of [large, large−51, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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(5¹⁰⁵, 4194302, F₅, 3, 11) (dual of [(4194302, 3), 12582801, 12]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(5¹⁰³, 4194301, F₅, 3, 11) (dual of [(4194301, 3), 12582800, 12]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(5¹⁰⁴, 4194301, F₅, 3, 11) (dual of [(4194301, 3), 12582799, 12]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(5¹⁰⁷, 4194307, F₅, 3, 11) (dual of [(4194307, 3), 12582814, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(5¹⁰⁸, 4194311, F₅, 3, 11) (dual of [(4194311, 3), 12582825, 12]-NRT-code)	[i]
6	Linear OOA(5¹⁰⁹, 4194322, F₅, 3, 11) (dual of [(4194322, 3), 12582857, 12]-NRT-code)	[i]
7	Linear OOA(5¹¹⁰, 4194334, F₅, 3, 11) (dual of [(4194334, 3), 12582892, 12]-NRT-code)	[i]
8	Linear OOA(5¹¹¹, 4194347, F₅, 3, 11) (dual of [(4194347, 3), 12582930, 12]-NRT-code)	[i]
9	Linear OOA(5¹¹², 4194369, F₅, 3, 11) (dual of [(4194369, 3), 12582995, 12]-NRT-code)	[i]
10	Linear OOA(5¹¹⁴, 4194395, F₅, 3, 11) (dual of [(4194395, 3), 12583071, 12]-NRT-code)	[i]
11	Linear OOA(5¹¹⁵, 4194601, F₅, 3, 11) (dual of [(4194601, 3), 12583688, 12]-NRT-code)	[i]
12	Linear OOA(5¹¹⁶, 4194901, F₅, 3, 11) (dual of [(4194901, 3), 12584587, 12]-NRT-code)	[i]
13	Linear OOA(5¹¹⁷, 4194902, F₅, 3, 11) (dual of [(4194902, 3), 12584589, 12]-NRT-code)	[i]
14	Linear OOA(5¹¹⁸, 4194907, F₅, 3, 11) (dual of [(4194907, 3), 12584603, 12]-NRT-code)	[i]
15	Linear OOA(5¹¹⁹, 4194932, F₅, 3, 11) (dual of [(4194932, 3), 12584677, 12]-NRT-code)	[i]
16	Linear OOA(5¹²⁰, 4195057, F₅, 3, 11) (dual of [(4195057, 3), 12585051, 12]-NRT-code)	[i]
17	Linear OOA(5¹⁴², 8388602, F₅, 3, 11) (dual of [(8388602, 3), 25165664, 12]-NRT-code)	[i]
18	Linear OOA(5¹¹⁴, 4194396, F₅, 3, 11) (dual of [(4194396, 3), 12583074, 12]-NRT-code)	[i]