MinT - Information on Result #880361

Information on Result #880361

Linear OOA(256⁶⁰, 32782, F₂₅₆, 2, 26) (dual of [(32782, 2), 65504, 27]-NRT-code), using OOA 2-folding based on linear OA(256⁶⁰, 65564, F₂₅₆, 26) (dual of [65564, 65504, 27]-code), using

discarding factors / shortening the dual code based on linear OA(256⁶⁰, 65565, F₂₅₆, 26) (dual of [65565, 65505, 27]-code), using
- constructionÂ X applied to C_e(25) âŠ‚ C_e(15) [i] based on
  1. linear OA(256⁵¹, 65536, F₂₅₆, 26) (dual of [65536, 65485, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
  2. linear OA(256³¹, 65536, F₂₅₆, 16) (dual of [65536, 65505, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(256⁹, 29, F₂₅₆, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁹, 256, F₂₅₆, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
      - Reedâ€“Solomon code RS(247,256) [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(256⁶⁰, 32782, F₂₅₆, 3, 26) (dual of [(32782, 3), 98286, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁶⁰, 32782, F₂₅₆, 4, 26) (dual of [(32782, 4), 131068, 27]-NRT-code)	[i]
3	Linear OOA(256⁶⁰, 32782, F₂₅₆, 5, 26) (dual of [(32782, 5), 163850, 27]-NRT-code)	[i]
4	Linear OOA(256⁶⁰, 32782, F₂₅₆, 6, 26) (dual of [(32782, 6), 196632, 27]-NRT-code)	[i]
5	Digital (34, 60, 32782)-net over F₂₅₆	[i]