MinT - Information on Result #1615374

Information on Result #1615374

Linear OOA(256³², 21849, F₂₅₆, 4, 15) (dual of [(21849, 4), 87364, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256³², 21849, F₂₅₆, 3, 15) (dual of [(21849, 3), 65515, 16]-NRT-code), using

OOA 3-folding [i] 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: 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	OOA(128³⁷, 21849, S₁₂₈, 4, 15)	[i]		Discarding Parts of the Base for OOAs
2	Linear OOA(256³², 10924, F₂₅₆, 20, 15) (dual of [(10924, 20), 218448, 16]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row