MinT - Information on Result #972252

Information on Result #972252

Linear OOA(5¹²², 4194301, F₅, 3, 13) (dual of [(4194301, 3), 12582781, 14]-NRT-code), using OOA 2-folding based on linear OOA(5¹²², 8388602, F₅, 2, 13) (dual of [(8388602, 2), 16777082, 14]-NRT-code), using

trace code [i] based on linear OOA(25⁶¹, 4194301, F₂₅, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁶¹, 8388602, F₂₅, 13) (dual of [8388602, 8388541, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁶¹, large, F₂₅, 13) (dual of [large, large−61, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(5¹²⁵, 4194302, F₅, 3, 13) (dual of [(4194302, 3), 12582781, 14]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(5¹²³, 4194301, F₅, 3, 13) (dual of [(4194301, 3), 12582780, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(5¹²⁴, 4194301, F₅, 3, 13) (dual of [(4194301, 3), 12582779, 14]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(5¹²⁸, 4194307, F₅, 3, 13) (dual of [(4194307, 3), 12582793, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(5¹²⁹, 4194311, F₅, 3, 13) (dual of [(4194311, 3), 12582804, 14]-NRT-code)	[i]
6	Linear OOA(5¹³⁰, 4194315, F₅, 3, 13) (dual of [(4194315, 3), 12582815, 14]-NRT-code)	[i]
7	Linear OOA(5¹³¹, 4194328, F₅, 3, 13) (dual of [(4194328, 3), 12582853, 14]-NRT-code)	[i]
8	Linear OOA(5¹³², 4194334, F₅, 3, 13) (dual of [(4194334, 3), 12582870, 14]-NRT-code)	[i]
9	Linear OOA(5¹³⁴, 4194353, F₅, 3, 13) (dual of [(4194353, 3), 12582925, 14]-NRT-code)	[i]
10	Linear OOA(5¹³⁵, 4194354, F₅, 3, 13) (dual of [(4194354, 3), 12582927, 14]-NRT-code)	[i]
11	Linear OOA(5¹³⁶, 4194360, F₅, 3, 13) (dual of [(4194360, 3), 12582944, 14]-NRT-code)	[i]
12	Linear OOA(5¹³⁷, 4194367, F₅, 3, 13) (dual of [(4194367, 3), 12582964, 14]-NRT-code)	[i]
13	Linear OOA(5¹³⁸, 4194405, F₅, 3, 13) (dual of [(4194405, 3), 12583077, 14]-NRT-code)	[i]
14	Linear OOA(5¹³⁹, 4194509, F₅, 3, 13) (dual of [(4194509, 3), 12583388, 14]-NRT-code)	[i]
15	Linear OOA(5¹⁴⁰, 4194511, F₅, 3, 13) (dual of [(4194511, 3), 12583393, 14]-NRT-code)	[i]