MinT - Information on Result #2612666

Information on Result #2612666

Linear OOA(2¹³⁹, 48, F₂, 3, 99) (dual of [(48, 3), 5, 100]-NRT-code), using strength reduction based on linear OOA(2¹³⁹, 48, F₂, 3, 100) (dual of [(48, 3), 5, 101]-NRT-code), using

juxtaposition [i] based on
1. 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]
2. 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 (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		This result only	Method
1	Linear OOA(2¹³⁹, 24, F₂, 6, 99) (dual of [(24, 6), 5, 100]-NRT-code)	[i]		OOA Folding