MinT - Information on Result #1665439

Information on Result #1665439

Linear OOA(2¹⁶¹, 2796329, F₂, 6, 12) (dual of [(2796329, 6), 16777813, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶¹, 2796329, F₂, 3, 12) (dual of [(2796329, 3), 8388826, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²³, 128, F₂, 3, 6) (dual of [(128, 3), 361, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²³, 128, F₂, 2, 6) (dual of [(128, 2), 233, 7]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹, 127, F₂, 2, 6) (dual of [(127, 2), 233, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]
2. linear OOA(2¹³⁸, 2796201, F₂, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(2¹⁶¹, 2796328, F₂, 7, 12) (dual of [(2796328, 7), 19574135, 13]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁶¹, 2796328, F₂, 8, 12) (dual of [(2796328, 8), 22370463, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁶¹, 2796328, F₂, 18, 12) (dual of [(2796328, 18), 50333743, 13]-NRT-code)	[i]