MinT - Information on Result #1049406

Information on Result #1049406

Linear OOA(2²⁵³, 86, F₂, 3, 181) (dual of [(86, 3), 5, 182]-NRT-code), using repeating each code word 2 times based on linear OOA(2¹²⁴, 43, F₂, 3, 90) (dual of [(43, 3), 5, 91]-NRT-code), using

5 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), 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(2²⁵³, 86, F₂, 3, 180) (dual of [(86, 3), 5, 181]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁵³, 86, F₂, 3, 179) (dual of [(86, 3), 5, 180]-NRT-code)	[i]
3	Linear OOA(2²⁵³, 86, F₂, 3, 178) (dual of [(86, 3), 5, 179]-NRT-code)	[i]
4	Linear OOA(2²⁵³, 86, F₂, 3, 177) (dual of [(86, 3), 5, 178]-NRT-code)	[i]
5	Linear OOA(2²⁵³, 86, F₂, 3, 176) (dual of [(86, 3), 5, 177]-NRT-code)	[i]
6	Linear OOA(2²⁵³, 43, F₂, 6, 181) (dual of [(43, 6), 5, 182]-NRT-code)	[i]	OOA Folding