MinT - Information on Result #2455756

Information on Result #2455756

Linear OOA(2⁸², 44, F₂, 2, 53) (dual of [(44, 2), 6, 54]-NRT-code), using 2 step truncation based on linear OOA(2⁸⁴, 45, F₂, 2, 55) (dual of [(45, 2), 6, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
  - extended Reedâ€“Solomon code RS_e(2,8) [i]
  - Simplex code S(2,8) [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(2²⁵⁸, 132, F₂, 2, 161) (dual of [(132, 2), 6, 162]-NRT-code)	[i]	Repeating Each Code Word for NRT-Codes
2	Linear OOA(2¹⁷⁸, 92, F₂, 2, 113) (dual of [(92, 2), 6, 114]-NRT-code)	[i]	Juxtaposition for OOAs
3	Linear OOA(2²⁰⁸, 107, F₂, 2, 133) (dual of [(107, 2), 6, 134]-NRT-code)	[i]
4	Linear OOA(2²²⁴, 115, F₂, 2, 141) (dual of [(115, 2), 6, 142]-NRT-code)	[i]
5	Linear OOA(2⁸², 22, F₂, 4, 53) (dual of [(22, 4), 6, 54]-NRT-code)	[i]	OOA Folding