MinT - Information on Result #1567598

Information on Result #1567598

Linear OOA(256⁵⁶, 28927, F₂₅₆, 3, 25) (dual of [(28927, 3), 86725, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵⁶, 28927, F₂₅₆, 2, 25) (dual of [(28927, 2), 57798, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁵⁶, 32780, F₂₅₆, 2, 25) (dual of [(32780, 2), 65504, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁵⁶, 65560, F₂₅₆, 25) (dual of [65560, 65504, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(256³³, 65537, F₂₅₆, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    3. linear OA(256⁷, 23, F₂₅₆, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁷, 256, F₂₅₆, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
        Reedâ€“Solomon code RS(249,256) [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(256⁵⁶, 14463, F₂₅₆, 5, 25) (dual of [(14463, 5), 72259, 26]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256⁵⁶, 14463, F₂₅₆, 6, 25) (dual of [(14463, 6), 86722, 26]-NRT-code)	[i]		OOA Folding