MinT - Information on Result #1117445

Information on Result #1117445

Linear OOA(3²⁴², 6068264, F₃, 5, 13) (dual of [(6068264, 5), 30341078, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁵, 2796221, F₃, 5, 6) (dual of [(2796221, 5), 13981040, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 5, 3) (dual of [(20, 5), 95, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on 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, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
    - OA 3-folding and stacking [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(3¹⁷⁷, 3272043, F₃, 5, 13) (dual of [(3272043, 5), 16360038, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵⁶, 1594323, F₃, 5, 6) (dual of [(1594323, 5), 7971559, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁵⁶, 4782969, F₃, 6) (dual of [4782969, 4782913, 7]-code), using
      - 1 times truncation [i] based on linear OA(3⁵⁷, 4782970, F₃, 7) (dual of [4782970, 4782913, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  2. linear OOA(3¹²¹, 1677720, F₃, 5, 13) (dual of [(1677720, 5), 8388479, 14]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(3¹²¹, 8388600, F₃, 13) (dual of [8388600, 8388479, 14]-code), using
      - discarding factors / shortening the dual code 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.