MinT - Information on Result #2419870

Information on Result #2419870

Linear OOA(2¹³⁴, 75, F₂, 2, 69) (dual of [(75, 2), 16, 70]-NRT-code), using strength reduction based on linear OOA(2¹³⁴, 75, F₂, 2, 71) (dual of [(75, 2), 16, 72]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹¹, 15, F₁₆, 11) (dual of [15, 4, 12]-code or 15-arc in PG(10,16)), using
  - discarding factors / shortening the dual code based on linear OA(16¹¹, 16, F₁₆, 11) (dual of [16, 5, 12]-code or 16-arc in PG(10,16)), using
    - Reedâ€“Solomon code RS(5,16) [i]
2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [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		Method
1	Linear OOA(2¹³³, 74, F₂, 2, 68) (dual of [(74, 2), 15, 69]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2¹³², 74, F₂, 2, 67) (dual of [(74, 2), 16, 68]-NRT-code)	[i]
3	Linear OOA(2¹³¹, 73, F₂, 2, 66) (dual of [(73, 2), 15, 67]-NRT-code)	[i]