MinT - Information on Result #894868

Information on Result #894868

Linear OOA(3⁵⁹, 4782984, F₃, 2, 5) (dual of [(4782984, 2), 9565909, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁵, 7174453, F₃, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- appending kth column [i] based on linear OA(3¹⁵, 7174453, F₃, 2) (dual of [7174453, 7174438, 3]-code), using
  - Hamming code H(15,3) [i]
linear OOA(3⁴⁴, 2391492, F₃, 2, 5) (dual of [(2391492, 2), 4782940, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁴⁴, 4782984, F₃, 5) (dual of [4782984, 4782940, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁴⁴, 4782985, F₃, 5) (dual of [4782985, 4782941, 6]-code), using
    - constructionÂ X4 applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(3⁴³, 4782969, F₃, 5) (dual of [4782969, 4782926, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3²⁹, 4782969, F₃, 4) (dual of [4782969, 4782940, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3¹⁵, 16, F₃, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
        dual of repetition code with length 16 [i]
      4. linear OA(3¹, 16, F₃, 1) (dual of [16, 15, 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]

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.