MinT - Information on Result #1049451

Information on Result #1049451

Linear OOA(2²⁰¹, 69, F₂, 3, 144) (dual of [(69, 3), 6, 145]-NRT-code), using juxtaposition based on

linear OOA(2⁶⁶, 24, F₂, 3, 48) (dual of [(24, 3), 6, 49]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(8⁶, 8, F₈, 6) (dual of [8, 2, 7]-code or 8-arc in PG(5,8)), using
    - Reedâ€“Solomon code RS(2,8) [i]
  2. linear OOA(2⁶, 3, F₂, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;3,2) [i]
linear OOA(2¹²⁹, 45, F₂, 3, 95) (dual of [(45, 3), 6, 96]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
    - extended Reedâ€“Solomon code RS_e(2,8) [i]
    - Simplex code S(2,8) [i]
  2. linear OOA(2¹², 5, F₂, 3, 11) (dual of [(5, 3), 3, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,3P) [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		This result only	Method
1	Linear OOA(2²⁰¹, 69, F₂, 3, 143) (dual of [(69, 3), 6, 144]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁰¹, 69, F₂, 3, 142) (dual of [(69, 3), 6, 143]-NRT-code)	[i]
3	Linear OOA(2²⁰¹, 69, F₂, 3, 141) (dual of [(69, 3), 6, 142]-NRT-code)	[i]
4	Linear OOA(2²⁰¹, 69, F₂, 3, 140) (dual of [(69, 3), 6, 141]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁹, 68, F₂, 3, 142) (dual of [(68, 3), 5, 143]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(2¹⁹³, 66, F₂, 3, 136) (dual of [(66, 3), 5, 137]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁰, 65, F₂, 3, 133) (dual of [(65, 3), 5, 134]-NRT-code)	[i]