MinT - Information on Result #2767765

Information on Result #2767765

Linear OOA(2²⁵², 65, F₂, 4, 186) (dual of [(65, 4), 8, 187]-NRT-code), using strength reduction based on linear OOA(2²⁵², 65, F₂, 4, 191) (dual of [(65, 4), 8, 192]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹¹, 13, F₁₆, 11) (dual of [13, 2, 12]-code or 13-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(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2²⁵³, 65, F₂, 4, 186) (dual of [(65, 4), 7, 187]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁹, 64, F₂, 4, 183) (dual of [(64, 4), 7, 184]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²⁴⁸, 64, F₂, 4, 182) (dual of [(64, 4), 8, 183]-NRT-code)	[i]
4	Linear OOA(2²⁴⁵, 63, F₂, 4, 179) (dual of [(63, 4), 7, 180]-NRT-code)	[i]
5	Linear OOA(2²⁴⁴, 63, F₂, 4, 178) (dual of [(63, 4), 8, 179]-NRT-code)	[i]
6	Linear OOA(2²⁴¹, 62, F₂, 4, 175) (dual of [(62, 4), 7, 176]-NRT-code)	[i]
7	Linear OOA(2²⁴⁰, 62, F₂, 4, 174) (dual of [(62, 4), 8, 175]-NRT-code)	[i]
8	Linear OOA(2²³⁷, 61, F₂, 4, 171) (dual of [(61, 4), 7, 172]-NRT-code)	[i]
9	Linear OOA(2²³⁶, 61, F₂, 4, 170) (dual of [(61, 4), 8, 171]-NRT-code)	[i]