MinT - Information on Result #2425102

Information on Result #2425102

Linear OOA(2²¹⁰, 125, F₂, 2, 88) (dual of [(125, 2), 40, 89]-NRT-code), using strength reduction based on linear OOA(2²¹⁰, 125, F₂, 2, 89) (dual of [(125, 2), 40, 90]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁷, 25, F₃₂, 17) (dual of [25, 8, 18]-code or 25-arc in PG(16,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁷, 32, F₃₂, 17) (dual of [32, 15, 18]-code or 32-arc in PG(16,32)), using
    - Reedâ€“Solomon code RS(15,32) [i]
2. linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;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(2²¹², 126, F₂, 2, 88) (dual of [(126, 2), 40, 89]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²¹¹, 125, F₂, 2, 88) (dual of [(125, 2), 39, 89]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁹, 124, F₂, 2, 87) (dual of [(124, 2), 39, 88]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁰⁸, 124, F₂, 2, 86) (dual of [(124, 2), 40, 87]-NRT-code)	[i]
5	Linear OOA(2²⁰⁷, 123, F₂, 2, 85) (dual of [(123, 2), 39, 86]-NRT-code)	[i]