MinT - Information on Result #2613572

Information on Result #2613572

Linear OOA(2¹⁵⁷, 55, F₂, 3, 108) (dual of [(55, 3), 8, 109]-NRT-code), using strength reduction based on linear OOA(2¹⁵⁷, 55, F₂, 3, 109) (dual of [(55, 3), 8, 110]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁹, 11, F₁₆, 9) (dual of [11, 2, 10]-code or 11-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(2¹⁵⁸, 55, F₂, 3, 108) (dual of [(55, 3), 7, 109]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁵⁵, 54, F₂, 3, 106) (dual of [(54, 3), 7, 107]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹⁵⁴, 54, F₂, 3, 105) (dual of [(54, 3), 8, 106]-NRT-code)	[i]
4	Linear OOA(2¹⁵², 53, F₂, 3, 103) (dual of [(53, 3), 7, 104]-NRT-code)	[i]
5	Linear OOA(2¹⁵¹, 53, F₂, 3, 102) (dual of [(53, 3), 8, 103]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁹, 52, F₂, 3, 100) (dual of [(52, 3), 7, 101]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁸, 52, F₂, 3, 99) (dual of [(52, 3), 8, 100]-NRT-code)	[i]
8	Linear OOA(2¹⁴⁶, 51, F₂, 3, 97) (dual of [(51, 3), 7, 98]-NRT-code)	[i]
9	Linear OOA(2¹⁴⁵, 51, F₂, 3, 96) (dual of [(51, 3), 8, 97]-NRT-code)	[i]
10	Linear OOA(2¹⁴³, 50, F₂, 3, 94) (dual of [(50, 3), 7, 95]-NRT-code)	[i]