MinT - Information on Result #2612937

Information on Result #2612937

Linear OOA(2¹⁴⁵, 55, F₂, 3, 78) (dual of [(55, 3), 20, 79]-NRT-code), using strength reduction based on linear OOA(2¹⁴⁵, 55, F₂, 3, 79) (dual of [(55, 3), 20, 80]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32⁷, 11, F₃₂, 7) (dual of [11, 4, 8]-code or 11-arc in PG(6,32)), using
  - discarding factors / shortening the dual code based on linear OA(32⁷, 32, F₃₂, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
    - Reedâ€“Solomon code RS(25,32) [i]
2. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [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(2¹⁴⁴, 54, F₂, 3, 77) (dual of [(54, 3), 18, 78]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2¹⁴³, 54, F₂, 3, 76) (dual of [(54, 3), 19, 77]-NRT-code)	[i]
3	Linear OOA(2¹⁴², 54, F₂, 3, 75) (dual of [(54, 3), 20, 76]-NRT-code)	[i]
4	Linear OOA(2¹⁴¹, 53, F₂, 3, 74) (dual of [(53, 3), 18, 75]-NRT-code)	[i]