MinT - Information on Result #1117491

Information on Result #1117491

Linear OOA(3¹⁸⁴, 1913192, F₃, 5, 14) (dual of [(1913192, 5), 9565776, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵⁷, 1594323, F₃, 5, 7) (dual of [(1594323, 5), 7971558, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [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(3¹²⁷, 956596, F₃, 5, 14) (dual of [(956596, 5), 4782853, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹²⁷, 4782980, F₃, 14) (dual of [4782980, 4782853, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁷, 4782983, F₃, 14) (dual of [4782983, 4782856, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(3¹²⁷, 4782969, F₃, 14) (dual of [4782969, 4782842, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.