MinT - Information on Result #1010678

Information on Result #1010678

Linear OOA(3¹⁹⁵, 5592428, F₃, 3, 13) (dual of [(5592428, 3), 16777089, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁵, 2796221, F₃, 3, 6) (dual of [(2796221, 3), 8388598, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. linear OOA(3⁶⁰, 2796201, F₃, 3, 6) (dual of [(2796201, 3), 8388543, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(3¹³⁰, 2796214, F₃, 3, 13) (dual of [(2796214, 3), 8388512, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁹, 13, F₃, 3, 6) (dual of [(13, 3), 30, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 9, 13)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹²¹, 2796201, F₃, 3, 13) (dual of [(2796201, 3), 8388482, 14]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.