MinT - Information on Result #893929

Information on Result #893929

Linear OOA(7³⁴, 5764804, F₇, 2, 5) (dual of [(5764804, 2), 11529574, 6]-NRT-code), using trace code based on linear OOA(49¹⁷, 2882402, F₄₉, 2, 5) (dual of [(2882402, 2), 5764787, 6]-NRT-code), using

OOA 2-folding [i] based on linear OA(49¹⁷, 5764804, F₄₉, 5) (dual of [5764804, 5764787, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49¹⁷, 5764805, F₄₉, 5) (dual of [5764805, 5764788, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. 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]
    2. 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]
    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(7³⁵, 5764804, F₇, 2, 5) (dual of [(5764804, 2), 11529573, 6]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7³⁷, 5764861, F₇, 2, 5) (dual of [(5764861, 2), 11529685, 6]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(7³⁸, 5765204, F₇, 2, 5) (dual of [(5765204, 2), 11530370, 6]-NRT-code)	[i]
4	Linear OOA(7³⁹, 5767605, F₇, 2, 5) (dual of [(5767605, 2), 11535171, 6]-NRT-code)	[i]
5	Linear OOA(7⁴⁰, 5784412, F₇, 2, 5) (dual of [(5784412, 2), 11568784, 6]-NRT-code)	[i]
6	Linear OOA(7⁴¹, 5902061, F₇, 2, 5) (dual of [(5902061, 2), 11804081, 6]-NRT-code)	[i]
7	Linear OOA(7⁴³, large, F₇, 2, 5)	[i]
8	Linear OOA(7³⁴, 5764803, F₇, 3, 5) (dual of [(5764803, 3), 17294375, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
9	Linear OOA(7³⁴, 5764803, F₇, 6, 5) (dual of [(5764803, 6), 34588784, 6]-NRT-code)	[i]	OOA Stacking with Additional Row