MinT - Information on Result #1049492

Information on Result #1049492

Linear OOA(2²⁴¹, 82, F₂, 3, 172) (dual of [(82, 3), 5, 173]-NRT-code), using juxtaposition based on

linear OOA(2¹⁰⁹, 38, F₂, 3, 78) (dual of [(38, 3), 5, 79]-NRT-code), using
- 5 step truncation [i] based on linear OOA(2¹¹⁴, 40, F₂, 3, 83) (dual of [(40, 3), 6, 84]-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(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]
linear OOA(2¹²⁷, 44, F₂, 3, 93) (dual of [(44, 3), 5, 94]-NRT-code), using
- 2 step truncation [i] based on 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) (see above)

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(2²⁴¹, 82, F₂, 3, 171) (dual of [(82, 3), 5, 172]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁴¹, 82, F₂, 3, 170) (dual of [(82, 3), 5, 171]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2²⁴¹, 41, F₂, 6, 172) (dual of [(41, 6), 5, 173]-NRT-code)	[i]		OOA Folding