MinT - Information on Result #972191

Information on Result #972191

Linear OOA(5¹¹², 4194301, F₅, 3, 12) (dual of [(4194301, 3), 12582791, 13]-NRT-code), using OOA 2-folding based on linear OOA(5¹¹², 8388602, F₅, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using

trace code [i] based on linear OOA(25⁵⁶, 4194301, F₂₅, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵⁶, 8388602, F₂₅, 12) (dual of [8388602, 8388546, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(5¹¹⁵, 4194302, F₅, 3, 12) (dual of [(4194302, 3), 12582791, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(5¹¹³, 4194301, F₅, 3, 12) (dual of [(4194301, 3), 12582790, 13]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(5¹¹⁴, 4194301, F₅, 3, 12) (dual of [(4194301, 3), 12582789, 13]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(5¹¹⁸, 4194307, F₅, 3, 12) (dual of [(4194307, 3), 12582803, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(5¹¹⁹, 4194311, F₅, 3, 12) (dual of [(4194311, 3), 12582814, 13]-NRT-code)	[i]
6	Linear OOA(5¹²⁰, 4194315, F₅, 3, 12) (dual of [(4194315, 3), 12582825, 13]-NRT-code)	[i]
7	Linear OOA(5¹²¹, 4194328, F₅, 3, 12) (dual of [(4194328, 3), 12582863, 13]-NRT-code)	[i]
8	Linear OOA(5¹²², 4194334, F₅, 3, 12) (dual of [(4194334, 3), 12582880, 13]-NRT-code)	[i]
9	Linear OOA(5¹²⁴, 4194353, F₅, 3, 12) (dual of [(4194353, 3), 12582935, 13]-NRT-code)	[i]
10	Linear OOA(5¹²⁵, 4194354, F₅, 3, 12) (dual of [(4194354, 3), 12582937, 13]-NRT-code)	[i]
11	Linear OOA(5¹²⁶, 4194360, F₅, 3, 12) (dual of [(4194360, 3), 12582954, 13]-NRT-code)	[i]
12	Linear OOA(5¹²⁷, 4194367, F₅, 3, 12) (dual of [(4194367, 3), 12582974, 13]-NRT-code)	[i]
13	Linear OOA(5¹²⁸, 4194405, F₅, 3, 12) (dual of [(4194405, 3), 12583087, 13]-NRT-code)	[i]
14	Linear OOA(5¹²⁹, 4194509, F₅, 3, 12) (dual of [(4194509, 3), 12583398, 13]-NRT-code)	[i]
15	Linear OOA(5¹³⁰, 4194511, F₅, 3, 12) (dual of [(4194511, 3), 12583403, 13]-NRT-code)	[i]