MinT - Information on Result #2457248

Information on Result #2457248

Linear OOA(2¹¹², 64, F₂, 2, 54) (dual of [(64, 2), 16, 55]-NRT-code), using 2 step truncation based on linear OOA(2¹¹⁴, 65, F₂, 2, 56) (dual of [(65, 2), 16, 57]-NRT-code), using

strength reduction [i] based on linear OOA(2¹¹⁴, 65, F₂, 2, 59) (dual of [(65, 2), 16, 60]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16⁹, 13, F₁₆, 9) (dual of [13, 4, 10]-code or 13-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(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		This result only	Method
1	Linear OOA(2¹¹², 32, F₂, 4, 54) (dual of [(32, 4), 16, 55]-NRT-code)	[i]		OOA Folding