MinT - Information on Result #2652656

Information on Result #2652656

Linear OOA(2¹²⁷, 44, F₂, 3, 93) (dual of [(44, 3), 5, 94]-NRT-code), using 2 step truncation based on linear OOA(2¹²⁹, 45, F₂, 3, 95) (dual of [(45, 3), 6, 96]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
  - extended Reedâ€“Solomon code RS_e(2,8) [i]
  - Simplex code S(2,8) [i]
2. linear OOA(2¹², 5, F₂, 3, 11) (dual of [(5, 3), 3, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;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, 88, F₂, 3, 187) (dual of [(88, 3), 5, 188]-NRT-code)	[i]	Repeating Each Code Word for NRT-Codes
2	Linear OOA(2¹⁴², 49, F₂, 3, 103) (dual of [(49, 3), 5, 104]-NRT-code)	[i]	Juxtaposition for OOAs
3	Linear OOA(2¹⁹⁶, 67, F₂, 3, 140) (dual of [(67, 3), 5, 141]-NRT-code)	[i]
4	Linear OOA(2²⁰⁵, 70, F₂, 3, 147) (dual of [(70, 3), 5, 148]-NRT-code)	[i]
5	Linear OOA(2²⁴¹, 82, F₂, 3, 172) (dual of [(82, 3), 5, 173]-NRT-code)	[i]
6	Linear OOA(2²⁴⁴, 83, F₂, 3, 175) (dual of [(83, 3), 5, 176]-NRT-code)	[i]
7	Linear OOA(2¹²⁷, 22, F₂, 6, 93) (dual of [(22, 6), 5, 94]-NRT-code)	[i]	OOA Folding