MinT - Information on Result #2654680

Information on Result #2654680

Linear OOA(2²⁴⁰, 82, F₂, 3, 169) (dual of [(82, 3), 6, 170]-NRT-code), using 9 step truncation based on linear OOA(2²⁴⁹, 85, F₂, 3, 178) (dual of [(85, 3), 6, 179]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁴⁹, 85, F₂, 3, 179) (dual of [(85, 3), 6, 180]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. 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]
  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(2²⁴⁰, 41, F₂, 6, 169) (dual of [(41, 6), 6, 170]-NRT-code)	[i]		OOA Folding