MinT - Information on Result #2616354

Information on Result #2616354

Linear OOA(2²⁰⁵, 70, F₂, 3, 146) (dual of [(70, 3), 5, 147]-NRT-code), using strength reduction based on linear OOA(2²⁰⁵, 70, F₂, 3, 147) (dual of [(70, 3), 5, 148]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁷³, 26, F₂, 3, 53) (dual of [(26, 3), 5, 54]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(2⁷⁵, 27, F₂, 3, 55) (dual of [(27, 3), 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(2⁶, 3, F₂, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;3,2) [i]
2. 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)) (see above)
      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(2²²⁰, 75, F₂, 3, 156) (dual of [(75, 3), 5, 157]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(2²⁰⁵, 35, F₂, 6, 146) (dual of [(35, 6), 5, 147]-NRT-code)	[i]		OOA Folding