MinT - Information on Result #1180841

Information on Result #1180841

Linear OOA(2²⁴², 2396797, F₂, 21, 14) (dual of [(2396797, 21), 50332495, 15]-NRT-code), using OOA stacking with additional row based on linear OOA(2²⁴², 2396798, F₂, 7, 14) (dual of [(2396798, 7), 16777344, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁷⁷, 1198399, F₂, 7, 14) (dual of [(1198399, 7), 8388616, 15]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁶, 28, F₂, 7, 7) (dual of [(28, 7), 180, 8]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁶, 28, F₂, 6, 7) (dual of [(28, 6), 152, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (9, 16, 28)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2¹⁶¹, 1198371, F₂, 7, 14) (dual of [(1198371, 7), 8388436, 15]-NRT-code), using
      - OOA 7-folding [i] based on linear OA(2¹⁶¹, 8388597, F₂, 14) (dual of [8388597, 8388436, 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (228, 242, 2396797)-net over F₂	[i]		Net Defined by OOA