MinT - Information on Result #1673244

Information on Result #1673244

Linear OOA(256⁶⁷, 13108, F₂₅₆, 6, 33) (dual of [(13108, 6), 78581, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁷, 13108, F₂₅₆, 5, 33) (dual of [(13108, 5), 65473, 34]-NRT-code), using

256¹ times duplication [i] based on linear OOA(256⁶⁶, 13108, F₂₅₆, 5, 33) (dual of [(13108, 5), 65474, 34]-NRT-code), using
- OOA 5-folding [i] based on linear OA(256⁶⁶, 65540, F₂₅₆, 33) (dual of [65540, 65474, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁶⁶, 65542, F₂₅₆, 33) (dual of [65542, 65476, 34]-code), using
    - constructionÂ X applied to C([0,16]) âŠ‚ C([0,15]) [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(256⁶¹, 65537, F₂₅₆, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (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(256⁶⁷, 4369, F₂₅₆, 42, 33) (dual of [(4369, 42), 183431, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row