MinT - Information on Result #1051629

Information on Result #1051629

Linear OOA(2¹⁷⁴, 2097158, F₂, 4, 14) (dual of [(2097158, 4), 8388458, 15]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁷⁴, 4194316, F₂, 2, 14) (dual of [(4194316, 2), 8388458, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁴, 4194317, F₂, 2, 14) (dual of [(4194317, 2), 8388460, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹³, 16, F₂, 2, 7) (dual of [(16, 2), 19, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 13, 16)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2¹⁷⁴, 2013126, F₂, 5, 14) (dual of [(2013126, 5), 10065456, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁴, 2013126, F₂, 6, 14) (dual of [(2013126, 6), 12078582, 15]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁴, 2013126, F₂, 7, 14) (dual of [(2013126, 7), 14091708, 15]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁴, 2013126, F₂, 8, 14) (dual of [(2013126, 8), 16104834, 15]-NRT-code)	[i]
5	Digital (160, 174, 2013126)-net over F₂	[i]