MinT - Information on Result #2617115

Information on Result #2617115

Linear OOA(2²¹⁷, 75, F₂, 3, 150) (dual of [(75, 3), 8, 151]-NRT-code), using strength reduction based on linear OOA(2²¹⁷, 75, F₂, 3, 153) (dual of [(75, 3), 8, 154]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹³, 15, F₁₆, 13) (dual of [15, 2, 14]-code or 15-arc in PG(12,16)), using
  - discarding factors / shortening the dual code based on linear OA(16¹³, 16, F₁₆, 13) (dual of [16, 3, 14]-code or 16-arc in PG(12,16)), using
    - Reedâ€“Solomon code RS(3,16) [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(2²¹⁶, 74, F₂, 3, 149) (dual of [(74, 3), 6, 150]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²¹⁵, 74, F₂, 3, 148) (dual of [(74, 3), 7, 149]-NRT-code)	[i]
3	Linear OOA(2²¹⁴, 74, F₂, 3, 147) (dual of [(74, 3), 8, 148]-NRT-code)	[i]
4	Linear OOA(2²¹³, 73, F₂, 3, 146) (dual of [(73, 3), 6, 147]-NRT-code)	[i]
5	Linear OOA(2²¹², 73, F₂, 3, 145) (dual of [(73, 3), 7, 146]-NRT-code)	[i]
6	Linear OOA(2²¹¹, 73, F₂, 3, 144) (dual of [(73, 3), 8, 145]-NRT-code)	[i]
7	Linear OOA(2²⁰⁹, 72, F₂, 3, 142) (dual of [(72, 3), 7, 143]-NRT-code)	[i]
8	Linear OOA(2²⁰⁸, 72, F₂, 3, 141) (dual of [(72, 3), 8, 142]-NRT-code)	[i]
9	Linear OOA(2²⁰⁷, 71, F₂, 3, 140) (dual of [(71, 3), 6, 141]-NRT-code)	[i]
10	Linear OOA(2²⁰⁶, 71, F₂, 3, 139) (dual of [(71, 3), 7, 140]-NRT-code)	[i]
11	Linear OOA(2²⁰⁵, 71, F₂, 3, 138) (dual of [(71, 3), 8, 139]-NRT-code)	[i]
12	Linear OOA(2²⁰³, 70, F₂, 3, 136) (dual of [(70, 3), 7, 137]-NRT-code)	[i]
13	Linear OOA(2²⁰⁰, 69, F₂, 3, 133) (dual of [(69, 3), 7, 134]-NRT-code)	[i]
14	Linear OOA(2¹⁹⁹, 69, F₂, 3, 132) (dual of [(69, 3), 8, 133]-NRT-code)	[i]