MinT - Information on Result #862004

Information on Result #862004

Linear OOA(25⁵², 313, F₂₅, 2, 28) (dual of [(313, 2), 574, 29]-NRT-code), using OOA 2-folding based on linear OA(25⁵², 626, F₂₅, 28) (dual of [626, 574, 29]-code), using

discarding factors / shortening the dual code based on linear OA(25⁵², 627, F₂₅, 28) (dual of [627, 575, 29]-code), using
- constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
  1. linear OA(25⁵², 625, F₂₅, 28) (dual of [625, 573, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  2. 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]
  3. linear OA(25⁰, 2, F₂₅, 0) (dual of [2, 2, 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(25⁶⁶, 339, F₂₅, 2, 28) (dual of [(339, 2), 612, 29]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(25⁶⁷, 340, F₂₅, 2, 28) (dual of [(340, 2), 613, 29]-NRT-code)	[i]
3	Linear OOA(25⁶⁸, 341, F₂₅, 2, 28) (dual of [(341, 2), 614, 29]-NRT-code)	[i]
4	Linear OOA(25⁶⁹, 365, F₂₅, 2, 28) (dual of [(365, 2), 661, 29]-NRT-code)	[i]
5	Linear OOA(25⁷⁰, 379, F₂₅, 2, 28) (dual of [(379, 2), 688, 29]-NRT-code)	[i]
6	Linear OOA(25⁷⁵, 417, F₂₅, 2, 28) (dual of [(417, 2), 759, 29]-NRT-code)	[i]
7	Linear OOA(25⁷⁶, 439, F₂₅, 2, 28) (dual of [(439, 2), 802, 29]-NRT-code)	[i]
8	Digital (24, 52, 253)-net over F₂₅	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound