MinT - Information on Result #2765131

Information on Result #2765131

Linear OOA(2²¹², 55, F₂, 4, 157) (dual of [(55, 4), 8, 158]-NRT-code), using strength reduction based on linear OOA(2²¹², 55, F₂, 4, 159) (dual of [(55, 4), 8, 160]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁹, 11, F₁₆, 9) (dual of [11, 2, 10]-code or 11-arc in PG(8,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
    - Reedâ€“Solomon code RS(7,16) [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(2²¹³, 55, F₂, 4, 157) (dual of [(55, 4), 7, 158]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁰⁹, 54, F₂, 4, 154) (dual of [(54, 4), 7, 155]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²⁰⁸, 54, F₂, 4, 153) (dual of [(54, 4), 8, 154]-NRT-code)	[i]
4	Linear OOA(2²⁰⁵, 53, F₂, 4, 150) (dual of [(53, 4), 7, 151]-NRT-code)	[i]
5	Linear OOA(2²⁰⁴, 53, F₂, 4, 149) (dual of [(53, 4), 8, 150]-NRT-code)	[i]
6	Linear OOA(2²⁰¹, 52, F₂, 4, 146) (dual of [(52, 4), 7, 147]-NRT-code)	[i]
7	Linear OOA(2²⁰⁰, 52, F₂, 4, 145) (dual of [(52, 4), 8, 146]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁷, 51, F₂, 4, 142) (dual of [(51, 4), 7, 143]-NRT-code)	[i]
9	Linear OOA(2¹⁸⁸, 49, F₂, 4, 133) (dual of [(49, 4), 8, 134]-NRT-code)	[i]