MinT - Information on Result #1049471

Information on Result #1049471

Linear OOA(2¹⁷⁸, 61, F₂, 3, 126) (dual of [(61, 3), 5, 127]-NRT-code), using juxtaposition based on

linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,5P) [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(2¹⁶³, 56, F₂, 3, 116) (dual of [(56, 3), 5, 117]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code) (see above)
  2. linear OOA(2¹⁴⁸, 51, F₂, 3, 106) (dual of [(51, 3), 5, 107]-NRT-code), using
    - strength reduction [i] based on linear OOA(2¹⁴⁸, 51, F₂, 3, 107) (dual of [(51, 3), 5, 108]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2¹³, 6, F₂, 3, 11) (dual of [(6, 3), 5, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
        an explicitly constructive algebraic function field [i]
        linear OOA(2¹³⁰, 45, F₂, 3, 95) (dual of [(45, 3), 5, 96]-NRT-code), using
        2¹ times duplication [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
        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 (see above)

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(2¹⁷⁸, 61, F₂, 3, 125) (dual of [(61, 3), 5, 126]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁷⁸, 61, F₂, 3, 124) (dual of [(61, 3), 5, 125]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁸, 61, F₂, 3, 123) (dual of [(61, 3), 5, 124]-NRT-code)	[i]