MinT - Information on Result #2614406

Information on Result #2614406

Linear OOA(2¹⁷², 60, F₂, 3, 117) (dual of [(60, 3), 8, 118]-NRT-code), using strength reduction based on linear OOA(2¹⁷², 60, F₂, 3, 120) (dual of [(60, 3), 8, 121]-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(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(2¹⁷⁰, 59, F₂, 3, 115) (dual of [(59, 3), 7, 116]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2¹⁶⁹, 59, F₂, 3, 114) (dual of [(59, 3), 8, 115]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁷, 58, F₂, 3, 112) (dual of [(58, 3), 7, 113]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁶, 58, F₂, 3, 111) (dual of [(58, 3), 8, 112]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁴, 57, F₂, 3, 109) (dual of [(57, 3), 7, 110]-NRT-code)	[i]
6	Linear OOA(2¹⁶³, 57, F₂, 3, 108) (dual of [(57, 3), 8, 109]-NRT-code)	[i]
7	Linear OOA(2¹⁶¹, 56, F₂, 3, 106) (dual of [(56, 3), 7, 107]-NRT-code)	[i]
8	Linear OOA(2¹⁶⁰, 56, F₂, 3, 105) (dual of [(56, 3), 8, 106]-NRT-code)	[i]
9	Linear OOA(2¹⁵⁸, 55, F₂, 3, 103) (dual of [(55, 3), 7, 104]-NRT-code)	[i]
10	Linear OOA(2¹⁵⁵, 54, F₂, 3, 100) (dual of [(54, 3), 7, 101]-NRT-code)	[i]
11	Linear OOA(2¹⁵⁴, 54, F₂, 3, 99) (dual of [(54, 3), 8, 100]-NRT-code)	[i]
12	Linear OOA(2¹⁷², 30, F₂, 6, 117) (dual of [(30, 6), 8, 118]-NRT-code)	[i]	OOA Folding