MinT - Information on Result #861927

Information on Result #861927

Linear OOA(25⁵⁰, 313, F₂₅, 2, 27) (dual of [(313, 2), 576, 28]-NRT-code), using OOA 2-folding based on linear OA(25⁵⁰, 626, F₂₅, 27) (dual of [626, 576, 28]-code), using

constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
1. linear OA(25⁵⁰, 625, F₂₅, 27) (dual of [625, 575, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
2. linear OA(25⁴⁹, 625, F₂₅, 26) (dual of [625, 576, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
3. linear OA(25⁰, 1, F₂₅, 0) (dual of [1, 1, 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(25⁵¹, 313, F₂₅, 2, 27) (dual of [(313, 2), 575, 28]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(25⁶³, 339, F₂₅, 2, 27) (dual of [(339, 2), 615, 28]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(25⁶⁴, 340, F₂₅, 2, 27) (dual of [(340, 2), 616, 28]-NRT-code)	[i]
4	Linear OOA(25⁶⁵, 341, F₂₅, 2, 27) (dual of [(341, 2), 617, 28]-NRT-code)	[i]
5	Linear OOA(25⁶⁶, 365, F₂₅, 2, 27) (dual of [(365, 2), 664, 28]-NRT-code)	[i]
6	Linear OOA(25⁶⁷, 379, F₂₅, 2, 27) (dual of [(379, 2), 691, 28]-NRT-code)	[i]
7	Linear OOA(25⁷², 417, F₂₅, 2, 27) (dual of [(417, 2), 762, 28]-NRT-code)	[i]
8	Linear OOA(25⁷³, 439, F₂₅, 2, 27) (dual of [(439, 2), 805, 28]-NRT-code)	[i]
9	Digital (23, 50, 244)-net over F₂₅	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound