MinT - Information on Result #1051876

Information on Result #1051876

Linear OOA(2²⁰⁹, 2097172, F₂, 4, 16) (dual of [(2097172, 4), 8388479, 17]-NRT-code), using OOA 2-folding based on linear OOA(2²⁰⁹, 4194344, F₂, 2, 16) (dual of [(4194344, 2), 8388479, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁹, 4194345, F₂, 2, 16) (dual of [(4194345, 2), 8388481, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁵, 44, F₂, 2, 8) (dual of [(44, 2), 63, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (17, 25, 44)-net over F₂, using
      - a net from the Salzburg tables [i]
  2. linear OOA(2¹⁸⁴, 4194301, F₂, 2, 16) (dual of [(4194301, 2), 8388418, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁸⁴, 8388602, F₂, 16) (dual of [8388602, 8388418, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and 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		Method
1	Linear OOA(2²⁰⁹, 2000393, F₂, 5, 16) (dual of [(2000393, 5), 10001756, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰⁹, 2000393, F₂, 6, 16) (dual of [(2000393, 6), 12002149, 17]-NRT-code)	[i]
3	Linear OOA(2²⁰⁹, 2000393, F₂, 7, 16) (dual of [(2000393, 7), 14002542, 17]-NRT-code)	[i]
4	Linear OOA(2²⁰⁹, 2000393, F₂, 8, 16) (dual of [(2000393, 8), 16002935, 17]-NRT-code)	[i]
5	Digital (193, 209, 2000393)-net over F₂	[i]