MinT - Information on Result #1698424

Information on Result #1698424

Linear OOA(2¹³⁶, 13115, F₂, 8, 17) (dual of [(13115, 8), 104784, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁶, 13115, F₂, 5, 17) (dual of [(13115, 5), 65439, 18]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹³⁶, 65575, F₂, 17) (dual of [65575, 65439, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹³⁶, 65576, F₂, 17) (dual of [65576, 65440, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(2¹²⁹, 65537, F₂, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(2⁹⁷, 65537, F₂, 13) (dual of [65537, 65440, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(2¹³⁶, 13114, F₂, 24, 17) (dual of [(13114, 24), 314600, 18]-NRT-code)	[i]		OOA Stacking with Additional Row