MinT - Information on Result #2781737

Information on Result #2781737

Linear OOA(2²²⁴, 58, F₂, 4, 166) (dual of [(58, 4), 8, 167]-NRT-code), using 8 step truncation based on linear OOA(2²³², 60, F₂, 4, 174) (dual of [(60, 4), 8, 175]-NRT-code), using

strength reduction [i] based on linear OOA(2²³², 60, F₂, 4, 175) (dual of [(60, 4), 8, 176]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹⁰, 12, F₁₆, 10) (dual of [12, 2, 11]-code or 12-arc in PG(9,16)), using
    - discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
      - Reedâ€“Solomon code RS(6,16) [i]
  2. linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;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(2²²⁴, 29, F₂, 8, 166) (dual of [(29, 8), 8, 167]-NRT-code)	[i]		OOA Folding