MinT - Information on Result #2419671

Information on Result #2419671

Linear OOA(2¹³⁰, 75, F₂, 2, 63) (dual of [(75, 2), 20, 64]-NRT-code), using strength reduction based on linear OOA(2¹³⁰, 75, F₂, 2, 65) (dual of [(75, 2), 20, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁰, 15, F₁₆, 10) (dual of [15, 5, 11]-code or 15-arc in PG(9,16)), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
    - Reedâ€“Solomon code RS(6,16) [i]
2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [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(2¹³¹, 75, F₂, 2, 63) (dual of [(75, 2), 19, 64]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹²⁹, 74, F₂, 2, 62) (dual of [(74, 2), 19, 63]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹²⁸, 74, F₂, 2, 61) (dual of [(74, 2), 20, 62]-NRT-code)	[i]
4	Linear OOA(2¹²⁷, 73, F₂, 2, 60) (dual of [(73, 2), 19, 61]-NRT-code)	[i]