MinT - Information on Result #942111

Information on Result #942111

Linear OOA(4²⁴⁷, 125, F₄, 2, 210) (dual of [(125, 2), 3, 211]-NRT-code), using juxtaposition based on

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]
linear OOA(4²²⁹, 116, F₄, 2, 195) (dual of [(116, 2), 3, 196]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code) (see above)
  2. linear OOA(4²¹¹, 107, F₄, 2, 180) (dual of [(107, 2), 3, 181]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code) (see above)
      2. linear OOA(4¹⁹³, 98, F₄, 2, 165) (dual of [(98, 2), 3, 166]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code) (see above)
        linear OOA(4¹⁷⁵, 89, F₄, 2, 150) (dual of [(89, 2), 3, 151]-NRT-code), using
        juxtaposition [i] based on
        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]
        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		Method
1	Linear OOA(4²⁴⁷, 125, F₄, 2, 209) (dual of [(125, 2), 3, 210]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²⁴⁴, 123, F₄, 2, 207) (dual of [(123, 2), 2, 208]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(4²⁴², 122, F₄, 2, 205) (dual of [(122, 2), 2, 206]-NRT-code)	[i]
4	Linear OOA(4²⁴⁰, 121, F₄, 2, 203) (dual of [(121, 2), 2, 204]-NRT-code)	[i]
5	Linear OOA(4²³⁶, 119, F₄, 2, 199) (dual of [(119, 2), 2, 200]-NRT-code)	[i]
6	Linear OOA(4²³⁴, 118, F₄, 2, 197) (dual of [(118, 2), 2, 198]-NRT-code)	[i]
7	Linear OOA(4²³², 117, F₄, 2, 195) (dual of [(117, 2), 2, 196]-NRT-code)	[i]