MinT - Information on Result #941815

Information on Result #941815

Linear OOA(3¹¹⁹, 61, F₃, 2, 95) (dual of [(61, 2), 3, 96]-NRT-code), using juxtaposition based on

linear OOA(3¹¹, 7, F₃, 2, 10) (dual of [(7, 2), 3, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁰⁵, 54, F₃, 2, 84) (dual of [(54, 2), 3, 85]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹¹, 7, F₃, 2, 10) (dual of [(7, 2), 3, 11]-NRT-code) (see above)
  2. linear OOA(3⁹¹, 47, F₃, 2, 73) (dual of [(47, 2), 3, 74]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,3) [i]
      2. linear OOA(3⁸³, 43, F₃, 2, 67) (dual of [(43, 2), 3, 68]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code) (see above)
        linear OOA(3⁷⁵, 39, F₃, 2, 61) (dual of [(39, 2), 3, 62]-NRT-code), using
        1 step truncation [i] based on linear OOA(3⁷⁶, 40, F₃, 2, 62) (dual of [(40, 2), 4, 63]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
        extended Reedâ€“Solomon code RS_e(2,9) [i]
        Simplex code S(2,9) [i]
        linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [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(3¹¹⁹, 61, F₃, 2, 94) (dual of [(61, 2), 3, 95]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹¹⁹, 61, F₃, 2, 93) (dual of [(61, 2), 3, 94]-NRT-code)	[i]
3	Linear OOA(3¹¹⁹, 61, F₃, 2, 92) (dual of [(61, 2), 3, 93]-NRT-code)	[i]
4	Linear OOA(3¹¹⁹, 61, F₃, 2, 91) (dual of [(61, 2), 3, 92]-NRT-code)	[i]
5	Linear OOA(3¹¹⁹, 61, F₃, 2, 90) (dual of [(61, 2), 3, 91]-NRT-code)	[i]
6	Linear OOA(3¹¹⁹, 61, F₃, 2, 89) (dual of [(61, 2), 3, 90]-NRT-code)	[i]
7	Linear OOA(3¹¹⁹, 61, F₃, 2, 88) (dual of [(61, 2), 3, 89]-NRT-code)	[i]
8	Linear OOA(3¹¹⁶, 59, F₃, 2, 92) (dual of [(59, 2), 2, 93]-NRT-code)	[i]	Truncation for OOAs
9	Linear OOA(3¹¹⁴, 58, F₃, 2, 90) (dual of [(58, 2), 2, 91]-NRT-code)	[i]	Truncation for OOAs
10	Linear OOA(3¹³³, 68, F₃, 2, 106) (dual of [(68, 2), 3, 107]-NRT-code)	[i]	Juxtaposition for OOAs