MinT - Information on Result #2767204

Information on Result #2767204

Linear OOA(2²⁴⁴, 64, F₂, 4, 164) (dual of [(64, 4), 12, 165]-NRT-code), using strength reduction based on linear OOA(2²⁴⁴, 64, F₂, 4, 167) (dual of [(64, 4), 12, 168]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹³, 16, F₁₆, 13) (dual of [16, 3, 14]-code or 16-arc in PG(12,16)), using
  - Reedâ€“Solomon code RS(3,16) [i]
2. linear OOA(2¹², 4, F₂, 4, 11) (dual of [(4, 4), 4, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹², 5, F₂, 4, 11) (dual of [(5, 4), 8, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,8P) [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(2²⁴⁴, 32, F₂, 8, 164) (dual of [(32, 8), 12, 165]-NRT-code)	[i]		OOA Folding