MinT - Information on Result #2470197

Information on Result #2470197

Linear OOA(4²³⁵, 120, F₄, 2, 188) (dual of [(120, 2), 5, 189]-NRT-code), using 2 step truncation based on linear OOA(4²³⁷, 121, F₄, 2, 190) (dual of [(121, 2), 5, 191]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁵⁹, 32, F₄, 2, 47) (dual of [(32, 2), 5, 48]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
    2. linear OOA(4¹⁵, 8, F₄, 2, 15) (dual of [(8, 2), 1, 16]-NRT-code), using
      - dual of repetition NRT-code with length 8 [i]
    3. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
2. linear OOA(4¹⁷³, 89, F₄, 2, 142) (dual of [(89, 2), 5, 143]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(4¹⁷⁴, 90, F₄, 2, 143) (dual of [(90, 2), 6, 144]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(16¹⁵, 18, F₁₆, 15) (dual of [18, 3, 16]-code or 18-arc in PG(14,16)), using
        Denniston code D(1,16) [i]
      2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁵³, 129, F₄, 2, 201) (dual of [(129, 2), 5, 202]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(4²⁵⁵, 130, F₄, 2, 202) (dual of [(130, 2), 5, 203]-NRT-code)	[i]		Juxtaposition for OOAs