MinT - Information on Result #993651

Information on Result #993651

Linear OOA(256³², 21849, F₂₅₆, 3, 15) (dual of [(21849, 3), 65515, 16]-NRT-code), using OOA 3-folding based on linear OA(256³², 65547, F₂₅₆, 15) (dual of [65547, 65515, 16]-code), using

discarding factors / shortening the dual code based on linear OA(256³², 65548, F₂₅₆, 15) (dual of [65548, 65516, 16]-code), using
- constructionÂ X applied to C([0,7]) âŠ‚ C([0,5]) [i] based on
  1. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
  2. linear OA(256²¹, 65537, F₂₅₆, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
  3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
    - discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
      - Reedâ€“Solomon code RS(253,256) [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(256³², 21849, F₂₅₆, 4, 15) (dual of [(21849, 4), 87364, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256³², 21849, F₂₅₆, 5, 15) (dual of [(21849, 5), 109213, 16]-NRT-code)	[i]
3	Linear OOA(256³², 21849, F₂₅₆, 6, 15) (dual of [(21849, 6), 131062, 16]-NRT-code)	[i]
4	Digital (17, 32, 21849)-net over F₂₅₆	[i]