MinT - Information on Result #993917

Information on Result #993917

Linear OOA(256⁵⁸, 21851, F₂₅₆, 3, 27) (dual of [(21851, 3), 65495, 28]-NRT-code), using OOA 3-folding based on linear OA(256⁵⁸, 65553, F₂₅₆, 27) (dual of [65553, 65495, 28]-code), using

discarding factors / shortening the dual code based on linear OA(256⁵⁸, 65554, F₂₅₆, 27) (dual of [65554, 65496, 28]-code), using
- constructionÂ X applied to C([0,13]) âŠ‚ C([0,10]) [i] based on
  1. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
  2. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  3. linear OA(256⁵, 17, F₂₅₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
      - Reedâ€“Solomon code RS(251,256) [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(256⁵⁸, 21210, F₂₅₆, 4, 27) (dual of [(21210, 4), 84782, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁵⁸, 21210, F₂₅₆, 5, 27) (dual of [(21210, 5), 105992, 28]-NRT-code)	[i]
3	Linear OOA(256⁵⁸, 21210, F₂₅₆, 6, 27) (dual of [(21210, 6), 127202, 28]-NRT-code)	[i]
4	Digital (31, 58, 21210)-net over F₂₅₆	[i]