MinT - Information on Result #2442456

Information on Result #2442456

Linear OOA(4¹⁹³, 98, F₄, 2, 162) (dual of [(98, 2), 3, 163]-NRT-code), using strength reduction based on linear OOA(4¹⁹³, 98, F₄, 2, 165) (dual of [(98, 2), 3, 166]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,3P) [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(4¹⁷⁵, 89, F₄, 2, 150) (dual of [(89, 2), 3, 151]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4⁷, 5, F₄, 2, 7) (dual of [(5, 2), 3, 8]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;3,4) [i]
    2. linear OOA(4¹⁶⁵, 84, F₄, 2, 142) (dual of [(84, 2), 3, 143]-NRT-code), using
      - 1 step truncation [i] based on linear OOA(4¹⁶⁶, 85, F₄, 2, 143) (dual of [(85, 2), 4, 144]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(16¹⁵, 17, F₁₆, 15) (dual of [17, 2, 16]-code or 17-arc in PG(14,16)), using
        extended Reedâ€“Solomon code RS_e(2,16) [i]
        Simplex code S(2,16) [i]
        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(4¹⁹⁹, 101, F₄, 2, 166) (dual of [(101, 2), 3, 167]-NRT-code)	[i]		Juxtaposition for OOAs