MinT - Information on Result #2614792

Information on Result #2614792

Linear OOA(2¹⁷⁹, 65, F₂, 3, 107) (dual of [(65, 3), 16, 108]-NRT-code), using strength reduction based on linear OOA(2¹⁷⁹, 65, F₂, 3, 109) (dual of [(65, 3), 16, 110]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁹, 13, F₁₆, 9) (dual of [13, 4, 10]-code or 13-arc in PG(8,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
    - Reedâ€“Solomon code RS(7,16) [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(2¹⁸⁰, 65, F₂, 3, 107) (dual of [(65, 3), 15, 108]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁷⁸, 64, F₂, 3, 106) (dual of [(64, 3), 14, 107]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹⁷⁷, 64, F₂, 3, 105) (dual of [(64, 3), 15, 106]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁶, 64, F₂, 3, 104) (dual of [(64, 3), 16, 105]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁵, 63, F₂, 3, 103) (dual of [(63, 3), 14, 104]-NRT-code)	[i]
6	Linear OOA(2¹⁷⁴, 63, F₂, 3, 102) (dual of [(63, 3), 15, 103]-NRT-code)	[i]
7	Linear OOA(2¹⁷², 62, F₂, 3, 100) (dual of [(62, 3), 14, 101]-NRT-code)	[i]
8	Linear OOA(2¹⁷¹, 62, F₂, 3, 99) (dual of [(62, 3), 15, 100]-NRT-code)	[i]
9	Linear OOA(2¹⁷⁰, 62, F₂, 3, 98) (dual of [(62, 3), 16, 99]-NRT-code)	[i]
10	Linear OOA(2¹⁶⁹, 61, F₂, 3, 97) (dual of [(61, 3), 14, 98]-NRT-code)	[i]
11	Linear OOA(2¹⁶⁸, 61, F₂, 3, 96) (dual of [(61, 3), 15, 97]-NRT-code)	[i]
12	Linear OOA(2¹⁶⁷, 61, F₂, 3, 95) (dual of [(61, 3), 16, 96]-NRT-code)	[i]
13	Linear OOA(2¹⁶⁶, 60, F₂, 3, 94) (dual of [(60, 3), 14, 95]-NRT-code)	[i]
14	Linear OOA(2¹⁶³, 59, F₂, 3, 91) (dual of [(59, 3), 14, 92]-NRT-code)	[i]
15	Linear OOA(2¹⁶², 59, F₂, 3, 90) (dual of [(59, 3), 15, 91]-NRT-code)	[i]