MinT - Information on Result #941951

Information on Result #941951

Linear OOA(4²³⁹, 122, F₄, 2, 191) (dual of [(122, 2), 5, 192]-NRT-code), using juxtaposition based on

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)
linear OOA(4¹⁷⁵, 90, F₄, 2, 143) (dual of [(90, 2), 5, 144]-NRT-code), using
- 4¹ times duplication [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(4²³⁵, 120, F₄, 2, 187) (dual of [(120, 2), 5, 188]-NRT-code)	[i]		Truncation for OOAs