MinT - Information on Result #1688276

Information on Result #1688276

Linear OOA(2²⁴¹, 5592424, F₂, 7, 15) (dual of [(5592424, 7), 39146727, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴¹, 5592424, F₂, 3, 15) (dual of [(5592424, 3), 16777031, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁷³, 2796212, F₂, 3, 15) (dual of [(2796212, 3), 8388463, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹¹, 11, F₂, 3, 7) (dual of [(11, 3), 22, 8]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 11, 11)-net over F₂, using
        a shift-net [i]
    2. linear OOA(2¹⁶², 2796201, F₂, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(2²⁴¹, 5592423, F₂, 8, 15) (dual of [(5592423, 8), 44739143, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2²⁴¹, 5592423, F₂, 21, 15) (dual of [(5592423, 21), 117440642, 16]-NRT-code)	[i]		OOA Stacking with Additional Row