MinT - Information on Result #2427764

Information on Result #2427764

Linear OOA(2²⁴⁰, 140, F₂, 2, 103) (dual of [(140, 2), 40, 104]-NRT-code), using strength reduction based on linear OOA(2²⁴⁰, 140, F₂, 2, 104) (dual of [(140, 2), 40, 105]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32²⁰, 28, F₃₂, 20) (dual of [28, 8, 21]-code or 28-arc in PG(19,32)), using
  - discarding factors / shortening the dual code based on linear OA(32²⁰, 32, F₃₂, 20) (dual of [32, 12, 21]-code or 32-arc in PG(19,32)), using
    - Reedâ€“Solomon code RS(12,32) [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(2²⁴², 141, F₂, 2, 103) (dual of [(141, 2), 40, 104]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁴¹, 140, F₂, 2, 103) (dual of [(140, 2), 39, 104]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²³⁹, 139, F₂, 2, 102) (dual of [(139, 2), 39, 103]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²³⁸, 139, F₂, 2, 101) (dual of [(139, 2), 40, 102]-NRT-code)	[i]
5	Linear OOA(2²³⁷, 138, F₂, 2, 100) (dual of [(138, 2), 39, 101]-NRT-code)	[i]
6	Linear OOA(2²⁴⁰, 70, F₂, 4, 103) (dual of [(70, 4), 40, 104]-NRT-code)	[i]	OOA Folding