MinT - Information on Result #2616630

Information on Result #2616630

Linear OOA(2²⁰⁹, 75, F₂, 3, 128) (dual of [(75, 3), 16, 129]-NRT-code), using strength reduction based on linear OOA(2²⁰⁹, 75, F₂, 3, 131) (dual of [(75, 3), 16, 132]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹¹, 15, F₁₆, 11) (dual of [15, 4, 12]-code or 15-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(2²⁰⁸, 74, F₂, 3, 127) (dual of [(74, 3), 14, 128]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁰⁷, 74, F₂, 3, 126) (dual of [(74, 3), 15, 127]-NRT-code)	[i]
3	Linear OOA(2²⁰⁶, 74, F₂, 3, 125) (dual of [(74, 3), 16, 126]-NRT-code)	[i]
4	Linear OOA(2²⁰⁵, 73, F₂, 3, 124) (dual of [(73, 3), 14, 125]-NRT-code)	[i]
5	Linear OOA(2²⁰⁴, 73, F₂, 3, 123) (dual of [(73, 3), 15, 124]-NRT-code)	[i]
6	Linear OOA(2²⁰³, 73, F₂, 3, 122) (dual of [(73, 3), 16, 123]-NRT-code)	[i]
7	Linear OOA(2²⁰², 72, F₂, 3, 121) (dual of [(72, 3), 14, 122]-NRT-code)	[i]
8	Linear OOA(2²⁰¹, 72, F₂, 3, 120) (dual of [(72, 3), 15, 121]-NRT-code)	[i]
9	Linear OOA(2¹⁹⁹, 71, F₂, 3, 118) (dual of [(71, 3), 14, 119]-NRT-code)	[i]
10	Linear OOA(2¹⁹⁸, 71, F₂, 3, 117) (dual of [(71, 3), 15, 118]-NRT-code)	[i]
11	Linear OOA(2¹⁹⁷, 71, F₂, 3, 116) (dual of [(71, 3), 16, 117]-NRT-code)	[i]
12	Linear OOA(2¹⁹⁶, 70, F₂, 3, 115) (dual of [(70, 3), 14, 116]-NRT-code)	[i]
13	Linear OOA(2¹⁹⁵, 70, F₂, 3, 114) (dual of [(70, 3), 15, 115]-NRT-code)	[i]
14	Linear OOA(2¹⁹³, 69, F₂, 3, 112) (dual of [(69, 3), 14, 113]-NRT-code)	[i]