MinT - Information on Result #873146

Information on Result #873146

Linear OOA(49¹⁷, 2882402, F₄₉, 2, 5) (dual of [(2882402, 2), 5764787, 6]-NRT-code), using OOA 2-folding 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(7³⁴, 5764804, F₇, 2, 5) (dual of [(5764804, 2), 11529574, 6]-NRT-code)	[i]	Trace Code for OOAs
2	Linear OOA(49¹⁹, 2882452, F₄₉, 2, 5) (dual of [(2882452, 2), 5764885, 6]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(49²⁰, 2884853, F₄₉, 2, 5) (dual of [(2884853, 2), 5769686, 6]-NRT-code)	[i]
4	Linear OOA(49²², 5764804, F₄₉, 2, 5) (dual of [(5764804, 2), 11529586, 6]-NRT-code)	[i]
5	Linear OOA(49⁵⁴, 5764804, F₄₉, 2, 10) (dual of [(5764804, 2), 11529554, 11]-NRT-code)	[i]
6	Linear OOA(49⁵⁵, 5764807, F₄₉, 2, 10) (dual of [(5764807, 2), 11529559, 11]-NRT-code)	[i]
7	Linear OOA(49²⁴, large, F₄₉, 2, 5)	[i]	Generalized (u,Â u+v)-Construction for OOAs
8	Linear OOA(49²³, large, F₄₉, 2, 5)	[i]	Generalized (u,Â u+v)-Construction for OOAs