MinT - Information on Result #2874623

Information on Result #2874623

Linear OOA(3²⁴⁷, 1679034, F₃, 5, 20) (dual of [(1679034, 5), 8394923, 21]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁴⁶, 1679034, F₃, 5, 20) (dual of [(1679034, 5), 8394924, 21]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁰, 1314, F₃, 5, 10) (dual of [(1314, 5), 6520, 11]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(3⁵⁰, 6570, F₃, 10) (dual of [6570, 6520, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
      1. linear OA(3⁴⁹, 6561, F₃, 10) (dual of [6561, 6512, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(3⁴¹, 6561, F₃, 8) (dual of [6561, 6520, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(3¹, 9, F₃, 1) (dual of [9, 8, 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(3¹⁹⁶, 1677720, F₃, 5, 20) (dual of [(1677720, 5), 8388404, 21]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(3¹⁹⁶, 8388600, F₃, 20) (dual of [8388600, 8388404, 21]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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.