MinT - Information on Result #1632058

Information on Result #1632058

Linear OOA(2¹³¹, 2097227, F₂, 5, 11) (dual of [(2097227, 5), 10486004, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³¹, 2097227, F₂, 4, 11) (dual of [(2097227, 4), 8388777, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹⁵, 77, F₂, 4, 5) (dual of [(77, 4), 293, 6]-NRT-code), using
  - extracting embedded OOA [i] based on digital (10, 15, 77)-net over F₂, using
    - linear code embedding found in a computer search [i]
2. linear OOA(2¹¹⁶, 2097150, F₂, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(2¹³¹, 2097226, F₂, 6, 11) (dual of [(2097226, 6), 12583225, 12]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹³¹, 2097226, F₂, 7, 11) (dual of [(2097226, 7), 14680451, 12]-NRT-code)	[i]
3	Linear OOA(2¹³¹, 2097226, F₂, 8, 11) (dual of [(2097226, 8), 16777677, 12]-NRT-code)	[i]
4	Linear OOA(2¹³¹, 2097226, F₂, 15, 11) (dual of [(2097226, 15), 31458259, 12]-NRT-code)	[i]