MinT - Information on Result #2224967

Information on Result #2224967

Linear OA(2¹³⁵, 65575, F₂, 16) (dual of [65575, 65440, 17]-code), using 1 times truncation 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: Constructive and 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		Method
1	Linear OOA(2¹³⁵, 32787, F₂, 2, 16) (dual of [(32787, 2), 65439, 17]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2¹³⁵, 21858, F₂, 3, 16) (dual of [(21858, 3), 65439, 17]-NRT-code)	[i]
3	Linear OOA(2¹³⁵, 16393, F₂, 4, 16) (dual of [(16393, 4), 65437, 17]-NRT-code)	[i]
4	Linear OOA(2¹³⁵, 13115, F₂, 5, 16) (dual of [(13115, 5), 65440, 17]-NRT-code)	[i]
5	Linear OOA(2¹³⁵, 10929, F₂, 6, 16) (dual of [(10929, 6), 65439, 17]-NRT-code)	[i]
6	Linear OOA(2¹³⁵, 9367, F₂, 7, 16) (dual of [(9367, 7), 65434, 17]-NRT-code)	[i]