MinT - Information on Result #1117172

Information on Result #1117172

Linear OOA(3⁸⁴, 35438, F₃, 5, 11) (dual of [(35438, 5), 177106, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶, 7, F₃, 5, 5) (dual of [(7, 5), 29, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁷⁸, 35431, F₃, 5, 11) (dual of [(35431, 5), 177077, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3⁷⁸, 177155, F₃, 11) (dual of [177155, 177077, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷⁸, 177158, F₃, 11) (dual of [177158, 177080, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(3⁷⁸, 177147, F₃, 11) (dual of [177147, 177069, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(3⁶⁷, 177147, F₃, 10) (dual of [177147, 177080, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and 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.