MinT - Information on Result #895562

Information on Result #895562

Linear OOA(4¹⁴⁸, 4194338, F₄, 2, 15) (dual of [(4194338, 2), 8388528, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁵, 37, F₄, 2, 7) (dual of [(37, 2), 59, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
      - ovoid in PG(3,Â 4) [i]
  2. linear OOA(4¹¹, 20, F₄, 2, 7) (dual of [(20, 2), 29, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 11, 20)-net over F₄, using
      - linear code embedding found in a computer search [i]
linear OOA(4¹³³, 4194301, F₄, 2, 15) (dual of [(4194301, 2), 8388469, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹³³, 8388602, F₄, 15) (dual of [8388602, 8388469, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

None.