MinT - Information on Result #1600023

Information on Result #1600023

Linear OOA(2²⁵¹, 3305872, F₂, 4, 16) (dual of [(3305872, 4), 13223237, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵¹, 3305872, F₂, 2, 16) (dual of [(3305872, 2), 6611493, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵¹, 4227078, F₂, 2, 16) (dual of [(4227078, 2), 8453905, 17]-NRT-code), using
- strength reduction [i] based on linear OOA(2²⁵¹, 4227078, F₂, 2, 17) (dual of [(4227078, 2), 8453905, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁶⁶, 32777, F₂, 2, 8) (dual of [(32777, 2), 65488, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2⁶⁶, 65554, F₂, 8) (dual of [65554, 65488, 9]-code), using
        strength reduction [i] based on linear OA(2⁶⁶, 65554, F₂, 9) (dual of [65554, 65488, 10]-code), using
        constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
        linear OA(2⁶⁵, 65536, F₂, 9) (dual of [65536, 65471, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2⁴⁹, 65536, F₂, 7) (dual of [65536, 65487, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
        dual of repetition code with length 18 [i]
        linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(2²⁵¹, 1652936, F₂, 7, 16) (dual of [(1652936, 7), 11570301, 17]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵¹, 1652936, F₂, 8, 16) (dual of [(1652936, 8), 13223237, 17]-NRT-code)	[i]		OOA Folding