MinT - Information on Result #2457003

Information on Result #2457003

Linear OOA(2¹¹⁰, 61, F₂, 2, 57) (dual of [(61, 2), 12, 58]-NRT-code), using 8 step truncation based on linear OOA(2¹¹⁸, 65, F₂, 2, 65) (dual of [(65, 2), 12, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁰, 13, F₁₆, 10) (dual of [13, 3, 11]-code or 13-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(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(2²²⁷, 118, F₂, 2, 114) (dual of [(118, 2), 9, 115]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²²⁷, 118, F₂, 2, 115) (dual of [(118, 2), 9, 116]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs