MinT - Information on Result #2417198

Information on Result #2417198

Linear OOA(2⁶⁴, 35, F₂, 2, 39) (dual of [(35, 2), 6, 40]-NRT-code), using strength reduction based on linear OOA(2⁶⁴, 35, F₂, 2, 41) (dual of [(35, 2), 6, 42]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁵, 7, F₈, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,8)), using
  - discarding factors / shortening the dual code based on linear OA(8⁵, 8, F₈, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,8)), using
    - Reedâ€“Solomon code RS(3,8) [i]
2. linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,3P) [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		Method
1	Linear OOA(2⁶³, 34, F₂, 2, 38) (dual of [(34, 2), 5, 39]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2⁶², 34, F₂, 2, 37) (dual of [(34, 2), 6, 38]-NRT-code)	[i]
3	Linear OOA(2⁶¹, 33, F₂, 2, 36) (dual of [(33, 2), 5, 37]-NRT-code)	[i]