MinT - Information on Result #2762718

Information on Result #2762718

Linear OOA(2¹⁷⁴, 45, F₂, 4, 134) (dual of [(45, 4), 6, 135]-NRT-code), using strength reduction based on linear OOA(2¹⁷⁴, 45, F₂, 4, 135) (dual of [(45, 4), 6, 136]-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(2¹⁷, 5, F₂, 4, 16) (dual of [(5, 4), 3, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2¹⁷³, 44, F₂, 4, 133) (dual of [(44, 4), 3, 134]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2¹⁷², 44, F₂, 4, 132) (dual of [(44, 4), 4, 133]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁰, 44, F₂, 4, 130) (dual of [(44, 4), 6, 131]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁶, 43, F₂, 4, 126) (dual of [(43, 4), 6, 127]-NRT-code)	[i]
5	Linear OOA(2¹⁶², 42, F₂, 4, 122) (dual of [(42, 4), 6, 123]-NRT-code)	[i]
6	Linear OOA(2¹⁵⁸, 41, F₂, 4, 118) (dual of [(41, 4), 6, 119]-NRT-code)	[i]