MinT - Information on Result #1008813

Information on Result #1008813

Linear OOA(7⁴², 3843202, F₇, 3, 6) (dual of [(3843202, 3), 11529564, 7]-NRT-code), using trace code based on linear OOA(49²¹, 1921601, F₄₉, 3, 6) (dual of [(1921601, 3), 5764782, 7]-NRT-code), using

OOA 3-folding [i] based on linear OA(49²¹, 5764803, F₄₉, 6) (dual of [5764803, 5764782, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(49²¹, 5764805, F₄₉, 6) (dual of [5764805, 5764784, 7]-code), using
  - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
    1. 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]
    2. linear OA(49¹⁷, 5764801, F₄₉, 5) (dual of [5764801, 5764784, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(7⁴³, 3843202, F₇, 3, 6) (dual of [(3843202, 3), 11529563, 7]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7⁴⁵, 3843210, F₇, 3, 6) (dual of [(3843210, 3), 11529585, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(7⁴⁶, 3843252, F₇, 3, 6) (dual of [(3843252, 3), 11529710, 7]-NRT-code)	[i]
4	Linear OOA(7⁴⁷, 3843334, F₇, 3, 6) (dual of [(3843334, 3), 11529955, 7]-NRT-code)	[i]
5	Linear OOA(7⁴⁸, 3843636, F₇, 3, 6) (dual of [(3843636, 3), 11530860, 7]-NRT-code)	[i]
6	Linear OOA(7⁴⁹, 3845701, F₇, 3, 6) (dual of [(3845701, 3), 11537054, 7]-NRT-code)	[i]
7	Linear OOA(7⁵⁰, 3849674, F₇, 3, 6) (dual of [(3849674, 3), 11548972, 7]-NRT-code)	[i]
8	Linear OOA(7⁵¹, 3864757, F₇, 3, 6) (dual of [(3864757, 3), 11594220, 7]-NRT-code)	[i]
9	Linear OOA(7⁵⁵, 7686404, F₇, 3, 6) (dual of [(7686404, 3), 23059157, 7]-NRT-code)	[i]
10	Linear OOA(7⁶³, 7700409, F₇, 3, 6) (dual of [(7700409, 3), 23101164, 7]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
11	Linear OOA(7⁶¹, 7687604, F₇, 3, 6) (dual of [(7687604, 3), 23062751, 7]-NRT-code)	[i]
12	Linear OOA(7⁶², 7694807, F₇, 3, 6) (dual of [(7694807, 3), 23084359, 7]-NRT-code)	[i]
13	Linear OOA(7⁶³, 7745228, F₇, 3, 6) (dual of [(7745228, 3), 23235621, 7]-NRT-code)	[i]
14	Linear OOA(7⁶⁴, 8098175, F₇, 3, 6) (dual of [(8098175, 3), 24294461, 7]-NRT-code)	[i]
15	Linear OOA(7⁵⁹, 7686518, F₇, 3, 6) (dual of [(7686518, 3), 23059495, 7]-NRT-code)	[i]
16	Linear OOA(7⁶⁰, 7687204, F₇, 3, 6) (dual of [(7687204, 3), 23061552, 7]-NRT-code)	[i]
17	Linear OOA(7⁶¹, 7692006, F₇, 3, 6) (dual of [(7692006, 3), 23075957, 7]-NRT-code)	[i]
18	Linear OOA(7⁶², 7725620, F₇, 3, 6) (dual of [(7725620, 3), 23176798, 7]-NRT-code)	[i]
19	Linear OOA(7⁶³, 7960918, F₇, 3, 6) (dual of [(7960918, 3), 23882691, 7]-NRT-code)	[i]
20	Linear OOA(7⁶⁴, large, F₇, 3, 6)	[i]
21	Linear OOA(7⁵⁸, 7686461, F₇, 3, 6) (dual of [(7686461, 3), 23059325, 7]-NRT-code)	[i]
22	Linear OOA(7⁵⁹, 7686804, F₇, 3, 6) (dual of [(7686804, 3), 23060353, 7]-NRT-code)	[i]
23	Linear OOA(7⁶⁰, 7689205, F₇, 3, 6) (dual of [(7689205, 3), 23067555, 7]-NRT-code)	[i]
24	Linear OOA(7⁶¹, 7706012, F₇, 3, 6) (dual of [(7706012, 3), 23117975, 7]-NRT-code)	[i]
25	Linear OOA(7⁶², 7823661, F₇, 3, 6) (dual of [(7823661, 3), 23470921, 7]-NRT-code)	[i]
26	Linear OOA(7⁶³, large, F₇, 3, 6)	[i]
27	Linear OOA(7⁴², 3843201, F₇, 9, 6) (dual of [(3843201, 9), 34588767, 7]-NRT-code)	[i]	OOA Stacking with Additional Row