MinT - Information on Result #1117280

Information on Result #1117280

Linear OOA(3¹⁵⁰, 1678454, F₃, 5, 12) (dual of [(1678454, 5), 8392120, 13]-NRT-code), using (u,Â u+v)-construction based on

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]
linear OOA(3¹²⁰, 1677720, F₃, 5, 12) (dual of [(1677720, 5), 8388480, 13]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹²⁰, 8388600, F₃, 12) (dual of [8388600, 8388480, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁰, large, F₃, 12) (dual of [large, large−120, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.