MinT - Information on Result #941953

Information on Result #941953

Linear OOA(4²⁵³, 129, F₄, 2, 202) (dual of [(129, 2), 5, 203]-NRT-code), using juxtaposition based on

linear OOA(4⁷⁵, 40, F₄, 2, 59) (dual of [(40, 2), 5, 60]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹⁶, 10, F₄, 2, 14) (dual of [(10, 2), 4, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4¹⁹, 10, F₄, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
    - dual of repetition NRT-code with length 10 [i]
  3. linear OOA(4²⁰, 10, F₄, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4²⁰, 10, F₄, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
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(4²⁵⁰, 127, F₄, 2, 199) (dual of [(127, 2), 4, 200]-NRT-code)	[i]		Truncation for OOAs