MinT - Information on Result #1119326

Information on Result #1119326

Linear OOA(3²⁰⁴, 4866365, F₃, 5, 13) (dual of [(4866365, 5), 24331621, 14]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3²⁷, 1594322, F₃, 5, 4) (dual of [(1594322, 5), 7971583, 5]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(3²⁷, 1594322, F₃, 4, 4) (dual of [(1594322, 4), 6377261, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(3²⁷, 1594322, F₃, 3, 4) (dual of [(1594322, 3), 4782939, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (23, 27, 1594322)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
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]
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.