MinT - Information on Result #1453871

Information on Result #1453871

Linear OOA(16⁷⁹, 1048595, F₁₆, 2, 16) (dual of [(1048595, 2), 2097111, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁷⁹, 1048595, F₁₆, 16) (dual of [1048595, 1048516, 17]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(16⁷⁸, 1048593, F₁₆, 16) (dual of [1048593, 1048515, 17]-code), using
  - 1 times truncation [i] based on linear OA(16⁷⁹, 1048594, F₁₆, 17) (dual of [1048594, 1048515, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(12) [i] based on
      1. linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(16⁶¹, 1048576, F₁₆, 13) (dual of [1048576, 1048515, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(16³, 18, F₁₆, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
        hyperoval in PG(2,Â 16) [i]
2. linear OA(16⁷⁸, 1048594, F₁₆, 15) (dual of [1048594, 1048516, 16]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16⁷⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 650622 878339 974728 321219 378393 058284 886491 433245 170642 370488 307256 660131 304835 129819 326696 [i]
3. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.