MinT - Information on Result #861952

Information on Result #861952

Linear OOA(25⁷⁶, 7814, F₂₅, 2, 27) (dual of [(7814, 2), 15552, 28]-NRT-code), using OOA 2-folding based on linear OA(25⁷⁶, 15628, F₂₅, 27) (dual of [15628, 15552, 28]-code), using

constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
1. linear OA(25⁷⁶, 15625, F₂₅, 27) (dual of [15625, 15549, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
2. linear OA(25⁷³, 15625, F₂₅, 26) (dual of [15625, 15552, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
3. linear OA(25⁰, 3, F₂₅, 0) (dual of [3, 3, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 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(25⁷⁷, 7814, F₂₅, 2, 27) (dual of [(7814, 2), 15551, 28]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(25⁸⁹, 7840, F₂₅, 2, 27) (dual of [(7840, 2), 15591, 28]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(25⁹⁰, 7841, F₂₅, 2, 27) (dual of [(7841, 2), 15592, 28]-NRT-code)	[i]
4	Linear OOA(25⁹¹, 7842, F₂₅, 2, 27) (dual of [(7842, 2), 15593, 28]-NRT-code)	[i]
5	Linear OOA(25⁹², 7866, F₂₅, 2, 27) (dual of [(7866, 2), 15640, 28]-NRT-code)	[i]
6	Linear OOA(25⁹³, 7880, F₂₅, 2, 27) (dual of [(7880, 2), 15667, 28]-NRT-code)	[i]
7	Linear OOA(25⁹⁸, 7918, F₂₅, 2, 27) (dual of [(7918, 2), 15738, 28]-NRT-code)	[i]
8	Linear OOA(25⁹⁹, 7940, F₂₅, 2, 27) (dual of [(7940, 2), 15781, 28]-NRT-code)	[i]
9	Digital (49, 76, 7814)-net over F₂₅	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound