MinT - Information on Result #1652948

Information on Result #1652948

Linear OOA(256⁴², 13975, F₂₅₆, 5, 21) (dual of [(13975, 5), 69833, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁴², 13975, F₂₅₆, 4, 21) (dual of [(13975, 4), 55858, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁴², 16385, F₂₅₆, 4, 21) (dual of [(16385, 4), 65498, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256⁴², 65540, F₂₅₆, 21) (dual of [65540, 65498, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁴², 65542, F₂₅₆, 21) (dual of [65542, 65500, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. 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]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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, 6987, F₂₅₆, 25, 21) (dual of [(6987, 25), 174633, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row