MinT - Information on Result #1683352

Information on Result #1683352

Linear OOA(2¹⁷⁴, 2013126, F₂, 7, 14) (dual of [(2013126, 7), 14091708, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁴, 2013126, F₂, 4, 14) (dual of [(2013126, 4), 8052330, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁴, 2097158, F₂, 4, 14) (dual of [(2097158, 4), 8388458, 15]-NRT-code), using
- OOA 2-folding [i] 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: 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(2¹⁷⁴, 2013125, F₂, 8, 14) (dual of [(2013125, 8), 16104826, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁷⁴, 2013125, F₂, 21, 14) (dual of [(2013125, 21), 42275451, 15]-NRT-code)	[i]		OOA Stacking with Additional Row