MinT - Information on Result #972317

Information on Result #972317

Linear OOA(5¹³², 4194301, F₅, 3, 14) (dual of [(4194301, 3), 12582771, 15]-NRT-code), using OOA 2-folding based on linear OOA(5¹³², 8388602, F₅, 2, 14) (dual of [(8388602, 2), 16777072, 15]-NRT-code), using

trace code [i] based on linear OOA(25⁶⁶, 4194301, F₂₅, 2, 14) (dual of [(4194301, 2), 8388536, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁶⁶, 8388602, F₂₅, 14) (dual of [8388602, 8388536, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁶⁶, large, F₂₅, 14) (dual of [large, large−66, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(5¹³⁵, 4194302, F₅, 3, 14) (dual of [(4194302, 3), 12582771, 15]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(5¹³⁸, 4194303, F₅, 3, 14) (dual of [(4194303, 3), 12582771, 15]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(5¹³³, 4194301, F₅, 3, 14) (dual of [(4194301, 3), 12582770, 15]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(5¹³⁴, 4194301, F₅, 3, 14) (dual of [(4194301, 3), 12582769, 15]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(5¹³⁹, 4194307, F₅, 3, 14) (dual of [(4194307, 3), 12582782, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
6	Linear OOA(5¹⁴⁰, 4194311, F₅, 3, 14) (dual of [(4194311, 3), 12582793, 15]-NRT-code)	[i]
7	Linear OOA(5¹⁴¹, 4194313, F₅, 3, 14) (dual of [(4194313, 3), 12582798, 15]-NRT-code)	[i]
8	Linear OOA(5¹⁴², 4194326, F₅, 3, 14) (dual of [(4194326, 3), 12582836, 15]-NRT-code)	[i]
9	Linear OOA(5¹⁴⁵, 4194332, F₅, 3, 14) (dual of [(4194332, 3), 12582851, 15]-NRT-code)	[i]
10	Linear OOA(5¹⁴⁶, 4194353, F₅, 3, 14) (dual of [(4194353, 3), 12582913, 15]-NRT-code)	[i]
11	Linear OOA(5¹⁴⁸, 4194355, F₅, 3, 14) (dual of [(4194355, 3), 12582917, 15]-NRT-code)	[i]
12	Linear OOA(5¹⁴⁹, 4194359, F₅, 3, 14) (dual of [(4194359, 3), 12582928, 15]-NRT-code)	[i]
13	Linear OOA(5¹⁵⁰, 4194379, F₅, 3, 14) (dual of [(4194379, 3), 12582987, 15]-NRT-code)	[i]
14	Linear OOA(5¹⁴⁸, 4194357, F₅, 3, 14) (dual of [(4194357, 3), 12582923, 15]-NRT-code)	[i]
15	Linear OOA(5¹⁴⁹, 4194376, F₅, 3, 14) (dual of [(4194376, 3), 12582979, 15]-NRT-code)	[i]
16	Linear OOA(5¹⁵⁰, 4194401, F₅, 3, 14) (dual of [(4194401, 3), 12583053, 15]-NRT-code)	[i]