MinT - Information on Result #941573

Information on Result #941573

Linear OOA(2¹⁷⁸, 92, F₂, 2, 113) (dual of [(92, 2), 6, 114]-NRT-code), using juxtaposition based on

linear OOA(2⁸², 44, F₂, 2, 53) (dual of [(44, 2), 6, 54]-NRT-code), using
- 2 step truncation [i] based on linear OOA(2⁸⁴, 45, F₂, 2, 55) (dual of [(45, 2), 6, 56]-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(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;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(2⁹⁰, 48, F₂, 2, 59) (dual of [(48, 2), 6, 60]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(4¹³, 16, F₄, 11) (dual of [16, 3, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
      - projective code from ovoid in PG(3,Â 4) [i]
  2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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(2¹⁷⁸, 92, F₂, 2, 112) (dual of [(92, 2), 6, 113]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁷⁸, 92, F₂, 2, 111) (dual of [(92, 2), 6, 112]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁸, 92, F₂, 2, 110) (dual of [(92, 2), 6, 111]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁸, 46, F₂, 4, 113) (dual of [(46, 4), 6, 114]-NRT-code)	[i]		OOA Folding