MinT - Information on Result #2619702

Information on Result #2619702

Linear OOA(2²⁵⁴, 90, F₂, 3, 153) (dual of [(90, 3), 16, 154]-NRT-code), using strength reduction based on linear OOA(2²⁵⁴, 90, F₂, 3, 155) (dual of [(90, 3), 16, 156]-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(2¹⁴, 6, F₂, 3, 12) (dual of [(6, 3), 4, 13]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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(2²⁵⁶, 90, F₂, 3, 153) (dual of [(90, 3), 14, 154]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵³, 89, F₂, 3, 152) (dual of [(89, 3), 14, 153]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²⁵², 89, F₂, 3, 151) (dual of [(89, 3), 15, 152]-NRT-code)	[i]
4	Linear OOA(2²⁵¹, 89, F₂, 3, 150) (dual of [(89, 3), 16, 151]-NRT-code)	[i]