MinT - Information on Result #2852382

Information on Result #2852382

Linear OOA(3¹⁵¹, 1678454, F₃, 5, 12) (dual of [(1678454, 5), 8392119, 13]-NRT-code), using strength reduction based on linear OOA(3¹⁵¹, 1678454, F₃, 5, 13) (dual of [(1678454, 5), 8392119, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3³⁰, 734, F₃, 5, 6) (dual of [(734, 5), 3640, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(3³⁰, 2202, F₃, 6) (dual of [2202, 2172, 7]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(3) [i] based on
      1. linear OA(3²⁹, 2187, F₃, 7) (dual of [2187, 2158, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3¹⁵, 2187, F₃, 4) (dual of [2187, 2172, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3¹, 15, F₃, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.