MinT - Information on Result #941997

Information on Result #941997

Linear OOA(4²¹², 108, F₄, 2, 177) (dual of [(108, 2), 4, 178]-NRT-code), using juxtaposition based on

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]
linear OOA(4¹⁹⁶, 100, F₄, 2, 165) (dual of [(100, 2), 4, 166]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code) (see above)
  2. linear OOA(4¹⁸⁰, 92, F₄, 2, 153) (dual of [(92, 2), 4, 154]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4¹⁰, 7, F₄, 2, 9) (dual of [(7, 2), 4, 10]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4¹⁰, 9, F₄, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9 (see above)
      2. 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(4²¹², 108, F₄, 2, 176) (dual of [(108, 2), 4, 177]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²¹², 108, F₄, 2, 175) (dual of [(108, 2), 4, 176]-NRT-code)	[i]		Strength Reduction for OOAs