MinT - Information on Result #896162

Information on Result #896162

Linear OOA(5¹¹⁶, 4194367, F₅, 2, 13) (dual of [(4194367, 2), 8388618, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁵, 66, F₅, 2, 6) (dual of [(66, 2), 117, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
      - caps completed using a computer search [i]
  2. linear OOA(5¹⁰, 33, F₅, 2, 6) (dual of [(33, 2), 56, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 33)-net over F₅, using
      - linear code embedding found in a computer search [i]
linear OOA(5¹⁰¹, 4194301, F₅, 2, 13) (dual of [(4194301, 2), 8388501, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁰¹, 8388602, F₅, 13) (dual of [8388602, 8388501, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

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