MinT - Information on Result #2620118

Information on Result #2620118

Linear OOA(2²⁵⁹, 89, F₂, 3, 178) (dual of [(89, 3), 8, 179]-NRT-code), using strength reduction based on linear OOA(2²⁵⁹, 89, F₂, 3, 179) (dual of [(89, 3), 8, 180]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁹, 9, F₂, 3, 14) (dual of [(9, 3), 8, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²³², 80, F₂, 3, 164) (dual of [(80, 3), 8, 165]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(16¹⁴, 16, F₁₆, 14) (dual of [16, 2, 15]-code or 16-arc in PG(13,16)), using
      - Reedâ€“Solomon code RS(2,16) [i]
    2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [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(2²⁵³, 87, F₂, 3, 172) (dual of [(87, 3), 8, 173]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵², 86, F₂, 3, 171) (dual of [(86, 3), 6, 172]-NRT-code)	[i]
3	Linear OOA(2²⁵¹, 86, F₂, 3, 170) (dual of [(86, 3), 7, 171]-NRT-code)	[i]
4	Linear OOA(2²⁵⁰, 86, F₂, 3, 169) (dual of [(86, 3), 8, 170]-NRT-code)	[i]
5	Linear OOA(2²⁴⁸, 85, F₂, 3, 167) (dual of [(85, 3), 7, 168]-NRT-code)	[i]