MinT - Information on Result #2654105

Information on Result #2654105

Linear OOA(2¹⁶², 58, F₂, 3, 100) (dual of [(58, 3), 12, 101]-NRT-code), using 6 step truncation based on linear OOA(2¹⁶⁸, 60, F₂, 3, 106) (dual of [(60, 3), 12, 107]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁶⁸, 60, F₂, 3, 109) (dual of [(60, 3), 12, 110]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16⁹, 12, F₁₆, 9) (dual of [12, 3, 10]-code or 12-arc in PG(8,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
      - Reedâ€“Solomon code RS(7,16) [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(2¹⁶², 29, F₂, 6, 100) (dual of [(29, 6), 12, 101]-NRT-code)	[i]		OOA Folding