MinT - Information on Result #1014098

Information on Result #1014098

Linear OOA(7¹⁰⁸, 5623, F₇, 3, 22) (dual of [(5623, 3), 16761, 23]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹⁷, 21, F₇, 3, 11) (dual of [(21, 3), 46, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁵, 8, F₇, 3, 5) (dual of [(8, 3), 19, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;19,7) [i]
  2. linear OOA(7¹², 13, F₇, 3, 11) (dual of [(13, 3), 27, 12]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 12, 13)-net over F₇, using
      - 1 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
linear OOA(7⁹¹, 5602, F₇, 3, 22) (dual of [(5602, 3), 16715, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁹¹, 16806, F₇, 22) (dual of [16806, 16715, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁹¹, 16807, F₇, 22) (dual of [16807, 16716, 23]-code), using
    - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

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