MinT - Information on Result #1010768

Information on Result #1010768

Linear OOA(3¹⁷⁶, 2796446, F₃, 3, 15) (dual of [(2796446, 3), 8389162, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁶, 245, F₃, 3, 7) (dual of [(245, 3), 709, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²⁶, 735, F₃, 7) (dual of [735, 709, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁶, 736, F₃, 7) (dual of [736, 710, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(4) [i] based on
      1. linear OA(3²⁵, 729, F₃, 7) (dual of [729, 704, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3¹⁹, 729, F₃, 5) (dual of [729, 710, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(3¹, 7, F₃, 1) (dual of [7, 6, 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(3¹⁵⁰, 2796201, F₃, 3, 15) (dual of [(2796201, 3), 8388453, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.