MinT - Information on Result #1013965

Information on Result #1013965

Linear OOA(7⁸⁴, 39237, F₇, 3, 15) (dual of [(39237, 3), 117627, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹¹, 21, F₇, 3, 7) (dual of [(21, 3), 52, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7³, 8, F₇, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;21,7) [i]
  2. linear OOA(7⁸, 13, F₇, 3, 7) (dual of [(13, 3), 31, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 8, 13)-net over F₇, using
      - 5 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
linear OOA(7⁷³, 39216, F₇, 3, 15) (dual of [(39216, 3), 117575, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁷³, 117648, F₇, 15) (dual of [117648, 117575, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁷³, 117649, F₇, 15) (dual of [117649, 117576, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 7⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

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