MinT - Information on Result #1008809

Information on Result #1008809

Linear OOA(7²⁶, 5764804, F₇, 3, 4) (dual of [(5764804, 3), 17294386, 5]-NRT-code), using trace code based on linear OOA(49¹³, 2882402, F₄₉, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using

OA 2-folding and stacking [i] based on linear OA(49¹³, 5764804, F₄₉, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(49¹³, 5764805, F₄₉, 4) (dual of [5764805, 5764792, 5]-code), using
  - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
    1. linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    2. linear OA(49⁹, 5764801, F₄₉, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(7²⁷, 5764804, F₇, 3, 4) (dual of [(5764804, 3), 17294385, 5]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7²⁸, 5764812, F₇, 3, 4) (dual of [(5764812, 3), 17294408, 5]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(7²⁹, 5764861, F₇, 3, 4) (dual of [(5764861, 3), 17294554, 5]-NRT-code)	[i]
4	Linear OOA(7³⁰, 5765204, F₇, 3, 4) (dual of [(5765204, 3), 17295582, 5]-NRT-code)	[i]
5	Linear OOA(7³¹, 5767605, F₇, 3, 4) (dual of [(5767605, 3), 17302784, 5]-NRT-code)	[i]
6	Linear OOA(7⁸⁴, 7686404, F₇, 3, 8) (dual of [(7686404, 3), 23059128, 9]-NRT-code)	[i]
7	Linear OOA(7⁸⁶, 7686412, F₇, 3, 8) (dual of [(7686412, 3), 23059150, 9]-NRT-code)	[i]
8	Linear OOA(7⁸⁸, 7686420, F₇, 3, 8) (dual of [(7686420, 3), 23059172, 9]-NRT-code)	[i]
9	Linear OOA(7⁸⁹, 7686430, F₇, 3, 8) (dual of [(7686430, 3), 23059201, 9]-NRT-code)	[i]
10	Linear OOA(7⁹⁰, 7686446, F₇, 3, 8) (dual of [(7686446, 3), 23059248, 9]-NRT-code)	[i]
11	Linear OOA(7⁹¹, 7686504, F₇, 3, 8) (dual of [(7686504, 3), 23059421, 9]-NRT-code)	[i]
12	Linear OOA(7⁹², 7686604, F₇, 3, 8) (dual of [(7686604, 3), 23059720, 9]-NRT-code)	[i]
13	Linear OOA(7⁹², 7686404, F₇, 3, 9) (dual of [(7686404, 3), 23059120, 10]-NRT-code)	[i]
14	Linear OOA(7⁹⁴, 7686416, F₇, 3, 9) (dual of [(7686416, 3), 23059154, 10]-NRT-code)	[i]
15	Linear OOA(7⁹⁶, 7686420, F₇, 3, 9) (dual of [(7686420, 3), 23059164, 10]-NRT-code)	[i]
16	Linear OOA(7⁹⁷, 7686430, F₇, 3, 9) (dual of [(7686430, 3), 23059193, 10]-NRT-code)	[i]
17	Linear OOA(7⁹⁸, 7686446, F₇, 3, 9) (dual of [(7686446, 3), 23059240, 10]-NRT-code)	[i]
18	Linear OOA(7⁹⁹, 7686504, F₇, 3, 9) (dual of [(7686504, 3), 23059413, 10]-NRT-code)	[i]
19	Linear OOA(7¹⁰⁰, 7686604, F₇, 3, 9) (dual of [(7686604, 3), 23059712, 10]-NRT-code)	[i]
20	Linear OOA(7¹⁰², 7686752, F₇, 3, 9) (dual of [(7686752, 3), 23060154, 10]-NRT-code)	[i]
21	Linear OOA(7¹⁰³, 7688756, F₇, 3, 9) (dual of [(7688756, 3), 23066165, 10]-NRT-code)	[i]
22	Linear OOA(7¹⁰⁴, 7691108, F₇, 3, 9) (dual of [(7691108, 3), 23073220, 10]-NRT-code)	[i]
23	Linear OOA(7²⁶, 5764804, F₇, 4, 4) (dual of [(5764804, 4), 23059190, 5]-NRT-code)	[i]	Appending kth Column