MinT - Information on Result #2916446

Information on Result #2916446

Linear OOA(2²⁵⁵, 43, F₂, 6, 229) (dual of [(43, 6), 3, 230]-NRT-code), using strength reduction based on linear OOA(2²⁵⁵, 43, F₂, 6, 231) (dual of [(43, 6), 3, 232]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁵, 3, F₂, 6, 15) (dual of [(3, 6), 3, 16]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(6;3,2) [i]
2. linear OOA(2²³⁷, 40, F₂, 6, 215) (dual of [(40, 6), 3, 216]-NRT-code), using
  - repeating each code word 8 times [i] based on linear OOA(2²⁷, 5, F₂, 6, 26) (dual of [(5, 6), 3, 27]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(6;F,3P) [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(2²⁵⁹, 43, F₂, 6, 229)	[i]	OOA Duplication
2	Linear OOA(2²⁶⁰, 43, F₂, 6, 229)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁴, 42, F₂, 6, 228)	[i]	Truncation for OOAs
4	Linear OOA(2²⁵³, 42, F₂, 6, 227)	[i]
5	Linear OOA(2²⁴⁸, 41, F₂, 6, 222)	[i]
6	Linear OOA(2²⁴⁷, 41, F₂, 6, 221)	[i]
7	Linear OOA(2²⁴⁴, 41, F₂, 6, 218) (dual of [(41, 6), 2, 219]-NRT-code)	[i]
8	Linear OOA(2²⁴², 40, F₂, 6, 216)	[i]
9	Linear OOA(2²⁴¹, 40, F₂, 6, 215)	[i]
10	Linear OOA(2²³⁶, 39, F₂, 6, 210)	[i]
11	Linear OOA(2²³⁵, 39, F₂, 6, 209)	[i]
12	Linear OOA(2²³⁰, 38, F₂, 6, 204)	[i]
13	Linear OOA(2²²⁹, 38, F₂, 6, 203)	[i]
14	Linear OOA(2²²⁴, 37, F₂, 6, 198)	[i]
15	Linear OOA(2²²³, 37, F₂, 6, 197)	[i]
16	Linear OOA(2²¹⁸, 36, F₂, 6, 192)	[i]
17	Linear OOA(2²¹⁷, 36, F₂, 6, 191)	[i]