MinT - Information on Result #1673264

Information on Result #1673264

Linear OOA(256⁶⁸, 14145, F₂₅₆, 6, 33) (dual of [(14145, 6), 84802, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁸, 14145, F₂₅₆, 4, 33) (dual of [(14145, 4), 56512, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁸, 16387, F₂₅₆, 4, 33) (dual of [(16387, 4), 65480, 34]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256⁶⁸, 65548, F₂₅₆, 33) (dual of [65548, 65480, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
    1. linear OA(256⁶⁵, 65537, F₂₅₆, 33) (dual of [65537, 65472, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    2. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (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: 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(256⁶⁸, 4714, F₂₅₆, 42, 33) (dual of [(4714, 42), 197920, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row