MinT - Information on Result #2766451

Information on Result #2766451

Linear OOA(2²³², 60, F₂, 4, 172) (dual of [(60, 4), 8, 173]-NRT-code), using strength reduction based on linear OOA(2²³², 60, F₂, 4, 175) (dual of [(60, 4), 8, 176]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁰, 12, F₁₆, 10) (dual of [12, 2, 11]-code or 12-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(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2²²⁹, 59, F₂, 4, 169) (dual of [(59, 4), 7, 170]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²²⁸, 59, F₂, 4, 168) (dual of [(59, 4), 8, 169]-NRT-code)	[i]
3	Linear OOA(2²²⁵, 58, F₂, 4, 165) (dual of [(58, 4), 7, 166]-NRT-code)	[i]
4	Linear OOA(2²²⁴, 58, F₂, 4, 164) (dual of [(58, 4), 8, 165]-NRT-code)	[i]
5	Linear OOA(2²²¹, 57, F₂, 4, 161) (dual of [(57, 4), 7, 162]-NRT-code)	[i]
6	Linear OOA(2²²⁰, 57, F₂, 4, 160) (dual of [(57, 4), 8, 161]-NRT-code)	[i]
7	Linear OOA(2²¹⁷, 56, F₂, 4, 157) (dual of [(56, 4), 7, 158]-NRT-code)	[i]
8	Linear OOA(2²¹⁶, 56, F₂, 4, 156) (dual of [(56, 4), 8, 157]-NRT-code)	[i]
9	Linear OOA(2²¹³, 55, F₂, 4, 153) (dual of [(55, 4), 7, 154]-NRT-code)	[i]
10	Linear OOA(2²⁰⁸, 54, F₂, 4, 148) (dual of [(54, 4), 8, 149]-NRT-code)	[i]
11	Linear OOA(2²⁰⁴, 53, F₂, 4, 144) (dual of [(53, 4), 8, 145]-NRT-code)	[i]
12	Linear OOA(2²³², 30, F₂, 8, 172) (dual of [(30, 8), 8, 173]-NRT-code)	[i]	OOA Folding