MinT - Information on Result #2615260

Information on Result #2615260

Linear OOA(2¹⁸⁷, 65, F₂, 3, 128) (dual of [(65, 3), 8, 129]-NRT-code), using strength reduction based on linear OOA(2¹⁸⁷, 65, F₂, 3, 131) (dual of [(65, 3), 8, 132]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹¹, 13, F₁₆, 11) (dual of [13, 2, 12]-code or 13-arc in PG(10,16)), using
  - discarding factors / shortening the dual code based on linear OA(16¹¹, 16, F₁₆, 11) (dual of [16, 5, 12]-code or 16-arc in PG(10,16)), using
    - Reedâ€“Solomon code RS(5,16) [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(2¹⁸⁵, 64, F₂, 3, 126) (dual of [(64, 3), 7, 127]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2¹⁸⁴, 64, F₂, 3, 125) (dual of [(64, 3), 8, 126]-NRT-code)	[i]
3	Linear OOA(2¹⁸², 63, F₂, 3, 123) (dual of [(63, 3), 7, 124]-NRT-code)	[i]
4	Linear OOA(2¹⁸¹, 63, F₂, 3, 122) (dual of [(63, 3), 8, 123]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁹, 62, F₂, 3, 120) (dual of [(62, 3), 7, 121]-NRT-code)	[i]
6	Linear OOA(2¹⁷⁸, 62, F₂, 3, 119) (dual of [(62, 3), 8, 120]-NRT-code)	[i]
7	Linear OOA(2¹⁷⁶, 61, F₂, 3, 117) (dual of [(61, 3), 7, 118]-NRT-code)	[i]
8	Linear OOA(2¹⁷⁵, 61, F₂, 3, 116) (dual of [(61, 3), 8, 117]-NRT-code)	[i]
9	Linear OOA(2¹⁷³, 60, F₂, 3, 114) (dual of [(60, 3), 7, 115]-NRT-code)	[i]
10	Linear OOA(2¹⁷⁰, 59, F₂, 3, 111) (dual of [(59, 3), 7, 112]-NRT-code)	[i]
11	Linear OOA(2¹⁶⁹, 59, F₂, 3, 110) (dual of [(59, 3), 8, 111]-NRT-code)	[i]