MinT - Information on Result #1598788

Information on Result #1598788

Linear OOA(2²³⁹, 1055, F₂, 4, 41) (dual of [(1055, 4), 3981, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁹, 1055, F₂, 2, 41) (dual of [(1055, 2), 1871, 42]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²³⁹, 2110, F₂, 41) (dual of [2110, 1871, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(2²³⁹, 2111, F₂, 41) (dual of [2111, 1872, 42]-code), using
  - constructionÂ X applied to C([0,20]) âŠ‚ C([0,16]) [i] based on
    1. linear OA(2²²¹, 2049, F₂, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
    2. linear OA(2¹⁷⁷, 2049, F₂, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    3. linear OA(2¹⁸, 62, F₂, 7) (dual of [62, 44, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸, 64, F₂, 7) (dual of [64, 46, 8]-code), using
        adding a parity check bit [i] based on linear OA(2¹⁷, 63, F₂, 6) (dual of [63, 46, 7]-code), using
        a â€œcyâ€ code from Brouwerâ€™s database [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(2²³⁹, 527, F₂, 7, 41) (dual of [(527, 7), 3450, 42]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²³⁹, 527, F₂, 8, 41) (dual of [(527, 8), 3977, 42]-NRT-code)	[i]		OOA Folding