MinT - Information on Result #2612654

Information on Result #2612654

Linear OOA(2¹³⁸, 50, F₂, 3, 85) (dual of [(50, 3), 12, 86]-NRT-code), using strength reduction based on linear OOA(2¹³⁸, 50, F₂, 3, 87) (dual of [(50, 3), 12, 88]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁷, 10, F₁₆, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁷, 16, F₁₆, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
    - Reedâ€“Solomon code RS(9,16) [i]
2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;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		This result only	Method
1	Linear OOA(2¹³⁸, 25, F₂, 6, 85) (dual of [(25, 6), 12, 86]-NRT-code)	[i]		OOA Folding