MinT - Information on Result #1008819

Information on Result #1008819

Linear OOA(7⁵⁰, 3843202, F₇, 3, 7) (dual of [(3843202, 3), 11529556, 8]-NRT-code), using trace code based on linear OOA(49²⁵, 1921601, F₄₉, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using

OOA 3-folding [i] based on linear OA(49²⁵, 5764803, F₄₉, 7) (dual of [5764803, 5764778, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(49²⁵, 5764805, F₄₉, 7) (dual of [5764805, 5764780, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(49²⁵, 5764801, F₄₉, 7) (dual of [5764801, 5764776, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(49²¹, 5764801, F₄₉, 6) (dual of [5764801, 5764780, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(7⁵¹, 3843202, F₇, 3, 7) (dual of [(3843202, 3), 11529555, 8]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7⁵³, 3843210, F₇, 3, 7) (dual of [(3843210, 3), 11529577, 8]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(7⁵⁴, 3843252, F₇, 3, 7) (dual of [(3843252, 3), 11529702, 8]-NRT-code)	[i]
4	Linear OOA(7⁵⁵, 3843334, F₇, 3, 7) (dual of [(3843334, 3), 11529947, 8]-NRT-code)	[i]
5	Linear OOA(7⁵⁶, 3843636, F₇, 3, 7) (dual of [(3843636, 3), 11530852, 8]-NRT-code)	[i]
6	Linear OOA(7⁵⁷, 3845701, F₇, 3, 7) (dual of [(3845701, 3), 11537046, 8]-NRT-code)	[i]
7	Linear OOA(7⁵⁸, 3849674, F₇, 3, 7) (dual of [(3849674, 3), 11548964, 8]-NRT-code)	[i]
8	Linear OOA(7⁵⁹, 3864757, F₇, 3, 7) (dual of [(3864757, 3), 11594212, 8]-NRT-code)	[i]
9	Linear OOA(7⁶⁰, 3965702, F₇, 3, 7) (dual of [(3965702, 3), 11897046, 8]-NRT-code)	[i]
10	Linear OOA(7⁶¹, 4166520, F₇, 3, 7) (dual of [(4166520, 3), 12499499, 8]-NRT-code)	[i]
11	Linear OOA(7⁶³, 7686404, F₇, 3, 7) (dual of [(7686404, 3), 23059149, 8]-NRT-code)	[i]
12	Linear OOA(7⁶⁹, 7687604, F₇, 3, 7) (dual of [(7687604, 3), 23062743, 8]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
13	Linear OOA(7⁷⁰, 7694807, F₇, 3, 7) (dual of [(7694807, 3), 23084351, 8]-NRT-code)	[i]
14	Linear OOA(7⁷¹, 7745228, F₇, 3, 7) (dual of [(7745228, 3), 23235613, 8]-NRT-code)	[i]
15	Linear OOA(7⁶⁷, 7686518, F₇, 3, 7) (dual of [(7686518, 3), 23059487, 8]-NRT-code)	[i]
16	Linear OOA(7⁶⁸, 7687204, F₇, 3, 7) (dual of [(7687204, 3), 23061544, 8]-NRT-code)	[i]
17	Linear OOA(7⁶⁹, 7692006, F₇, 3, 7) (dual of [(7692006, 3), 23075949, 8]-NRT-code)	[i]
18	Linear OOA(7⁷⁰, 7725620, F₇, 3, 7) (dual of [(7725620, 3), 23176790, 8]-NRT-code)	[i]
19	Linear OOA(7⁷¹, 7960918, F₇, 3, 7) (dual of [(7960918, 3), 23882683, 8]-NRT-code)	[i]
20	Linear OOA(7⁶⁶, 7686461, F₇, 3, 7) (dual of [(7686461, 3), 23059317, 8]-NRT-code)	[i]
21	Linear OOA(7⁶⁷, 7686804, F₇, 3, 7) (dual of [(7686804, 3), 23060345, 8]-NRT-code)	[i]
22	Linear OOA(7⁶⁸, 7689205, F₇, 3, 7) (dual of [(7689205, 3), 23067547, 8]-NRT-code)	[i]
23	Linear OOA(7⁶⁹, 7706012, F₇, 3, 7) (dual of [(7706012, 3), 23117967, 8]-NRT-code)	[i]
24	Linear OOA(7⁷⁰, 7823661, F₇, 3, 7) (dual of [(7823661, 3), 23470913, 8]-NRT-code)	[i]
25	Linear OOA(7⁷¹, large, F₇, 3, 7)	[i]
26	Linear OOA(7⁵⁰, 3843201, F₇, 9, 7) (dual of [(3843201, 9), 34588759, 8]-NRT-code)	[i]	OOA Stacking with Additional Row