MinT - Information on Result #2611107

Information on Result #2611107

Linear OOA(2⁹⁷, 35, F₂, 3, 64) (dual of [(35, 3), 8, 65]-NRT-code), using strength reduction based on linear OOA(2⁹⁷, 35, F₂, 3, 65) (dual of [(35, 3), 8, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁵, 7, F₁₆, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁵, 16, F₁₆, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
    - Reedâ€“Solomon code RS(11,16) [i]
2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;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		Method
1	Linear OOA(2⁹⁸, 35, F₂, 3, 64) (dual of [(35, 3), 7, 65]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2⁹⁵, 34, F₂, 3, 62) (dual of [(34, 3), 7, 63]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2⁹⁴, 34, F₂, 3, 61) (dual of [(34, 3), 8, 62]-NRT-code)	[i]
4	Linear OOA(2⁹², 33, F₂, 3, 59) (dual of [(33, 3), 7, 60]-NRT-code)	[i]
5	Linear OOA(2⁸⁸, 32, F₂, 3, 55) (dual of [(32, 3), 8, 56]-NRT-code)	[i]