MinT - Information on Result #2616034

Information on Result #2616034

Linear OOA(2²⁰⁰, 75, F₂, 3, 108) (dual of [(75, 3), 25, 109]-NRT-code), using strength reduction based on linear OOA(2²⁰⁰, 75, F₂, 3, 109) (dual of [(75, 3), 25, 110]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁰, 15, F₃₂, 10) (dual of [15, 5, 11]-code or 15-arc in PG(9,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁰, 32, F₃₂, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,32)), using
    - Reedâ€“Solomon code RS(22,32) [i]
2. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [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(2²⁰³, 76, F₂, 3, 108) (dual of [(76, 3), 25, 109]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁰², 75, F₂, 3, 108) (dual of [(75, 3), 23, 109]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁹, 74, F₂, 3, 107) (dual of [(74, 3), 23, 108]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2¹⁹⁸, 74, F₂, 3, 106) (dual of [(74, 3), 24, 107]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁷, 74, F₂, 3, 105) (dual of [(74, 3), 25, 106]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁶, 73, F₂, 3, 104) (dual of [(73, 3), 23, 105]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁵, 73, F₂, 3, 103) (dual of [(73, 3), 24, 104]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁴, 73, F₂, 3, 102) (dual of [(73, 3), 25, 103]-NRT-code)	[i]