MinT - Information on Result #1028226

Information on Result #1028226

Linear OOA(2²⁴⁹, 85, F₂, 3, 179) (dual of [(85, 3), 6, 180]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8¹⁵, 17, F₈, 14) (dual of [17, 2, 15]-code), using
- 1 times truncation [i] based on linear OA(8¹⁶, 18, F₈, 15) (dual of [18, 2, 16]-code), using
  - repeating each code word 2 times [i] based on 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]
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		Method
1	Linear OOA(2²⁴⁹, 85, F₂, 3, 178) (dual of [(85, 3), 6, 179]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁴⁹, 85, F₂, 3, 177) (dual of [(85, 3), 6, 178]-NRT-code)	[i]
3	Linear OOA(2²⁴⁹, 85, F₂, 3, 176) (dual of [(85, 3), 6, 177]-NRT-code)	[i]
4	Linear OOA(2²⁴⁹, 85, F₂, 3, 175) (dual of [(85, 3), 6, 176]-NRT-code)	[i]
5	Linear OOA(2²⁴⁹, 85, F₂, 3, 174) (dual of [(85, 3), 6, 175]-NRT-code)	[i]
6	Linear OOA(2²⁴⁹, 85, F₂, 3, 173) (dual of [(85, 3), 6, 174]-NRT-code)	[i]
7	Linear OOA(2²⁴⁹, 85, F₂, 3, 172) (dual of [(85, 3), 6, 173]-NRT-code)	[i]
8	Linear OOA(2²⁴⁹, 85, F₂, 3, 171) (dual of [(85, 3), 6, 172]-NRT-code)	[i]
9	Linear OOA(2²⁴⁹, 85, F₂, 3, 170) (dual of [(85, 3), 6, 171]-NRT-code)	[i]
10	Linear OOA(2²⁴⁹, 85, F₂, 3, 169) (dual of [(85, 3), 6, 170]-NRT-code)	[i]
11	Linear OOA(2²⁴⁹, 85, F₂, 3, 168) (dual of [(85, 3), 6, 169]-NRT-code)	[i]
12	Linear OOA(2²⁵⁰, 85, F₂, 3, 179) (dual of [(85, 3), 5, 180]-NRT-code)	[i]	OOA Duplication
13	Linear OOA(2²⁴⁸, 84, F₂, 3, 178) (dual of [(84, 3), 4, 179]-NRT-code)	[i]	Truncation for OOAs
14	Linear OOA(2²⁴⁷, 84, F₂, 3, 177) (dual of [(84, 3), 5, 178]-NRT-code)	[i]
15	Linear OOA(2²⁴⁶, 84, F₂, 3, 176) (dual of [(84, 3), 6, 177]-NRT-code)	[i]
16	Linear OOA(2²⁴³, 83, F₂, 3, 173) (dual of [(83, 3), 6, 174]-NRT-code)	[i]
17	Linear OOA(2²⁴⁰, 82, F₂, 3, 170) (dual of [(82, 3), 6, 171]-NRT-code)	[i]
18	Linear OOA(2²³⁵, 80, F₂, 3, 165) (dual of [(80, 3), 5, 166]-NRT-code)	[i]