MinT - Information on Result #1079651

Information on Result #1079651

Linear OOA(2²¹³, 4194314, F₂, 4, 12) (dual of [(4194314, 4), 16777043, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097149, F₂, 4, 6) (dual of [(2097149, 4), 8388532, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
  - 1 step truncation [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]
linear OOA(2¹⁴⁹, 2097165, F₂, 4, 12) (dual of [(2097165, 4), 8388511, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹¹, 15, F₂, 4, 6) (dual of [(15, 4), 49, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (5, 11, 15)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
      - discarding factors / shortening the dual code 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: Constructive and linear.

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