MinT - Information on Result #2768367

Information on Result #2768367

Linear OOA(2²⁶⁰, 68, F₂, 4, 178) (dual of [(68, 4), 12, 179]-NRT-code), using strength reduction based on linear OOA(2²⁶⁰, 68, F₂, 4, 179) (dual of [(68, 4), 12, 180]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁴, 17, F₁₆, 14) (dual of [17, 3, 15]-code or 17-arc in PG(13,16)), using
  - extended Reedâ€“Solomon code RS_e(3,16) [i]
2. linear OOA(2¹², 4, F₂, 4, 11) (dual of [(4, 4), 4, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹², 5, F₂, 4, 11) (dual of [(5, 4), 8, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,8P) [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(2²⁵⁸, 67, F₂, 4, 176) (dual of [(67, 4), 10, 177]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵⁷, 67, F₂, 4, 175) (dual of [(67, 4), 11, 176]-NRT-code)	[i]
3	Linear OOA(2²⁵⁶, 67, F₂, 4, 174) (dual of [(67, 4), 12, 175]-NRT-code)	[i]
4	Linear OOA(2²⁵⁴, 66, F₂, 4, 172) (dual of [(66, 4), 10, 173]-NRT-code)	[i]
5	Linear OOA(2²⁵³, 66, F₂, 4, 171) (dual of [(66, 4), 11, 172]-NRT-code)	[i]
6	Linear OOA(2²⁴⁹, 65, F₂, 4, 167) (dual of [(65, 4), 11, 168]-NRT-code)	[i]
7	Linear OOA(2²⁶⁰, 34, F₂, 8, 178) (dual of [(34, 8), 12, 179]-NRT-code)	[i]	OOA Folding