MinT - Information on Result #1567423

Information on Result #1567423

Linear OOA(256⁴², 27957, F₂₅₆, 3, 19) (dual of [(27957, 3), 83829, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁴², 27957, F₂₅₆, 2, 19) (dual of [(27957, 2), 55872, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁴², 32777, F₂₅₆, 2, 19) (dual of [(32777, 2), 65512, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁴², 65554, F₂₅₆, 19) (dual of [65554, 65512, 20]-code), using
  - constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(256³⁷, 65537, F₂₅₆, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    2. linear OA(256²⁵, 65537, F₂₅₆, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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: 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		This result only	Method
1	Linear OOA(256⁴², 13978, F₂₅₆, 5, 19) (dual of [(13978, 5), 69848, 20]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256⁴², 13978, F₂₅₆, 6, 19) (dual of [(13978, 6), 83826, 20]-NRT-code)	[i]		OOA Folding