MinT - Information on Result #2618623

Information on Result #2618623

Linear OOA(2²³⁹, 85, F₂, 3, 149) (dual of [(85, 3), 16, 150]-NRT-code), using strength reduction based on linear OOA(2²³⁹, 85, F₂, 3, 153) (dual of [(85, 3), 16, 154]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹³, 17, F₁₆, 13) (dual of [17, 4, 14]-code or 17-arc in PG(12,16)), using
  - extended Reedâ€“Solomon code RS_e(4,16) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;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(2²⁴⁰, 85, F₂, 3, 149) (dual of [(85, 3), 15, 150]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴¹, 85, F₂, 3, 149) (dual of [(85, 3), 14, 150]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²³⁸, 84, F₂, 3, 148) (dual of [(84, 3), 14, 149]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²³⁷, 84, F₂, 3, 147) (dual of [(84, 3), 15, 148]-NRT-code)	[i]
5	Linear OOA(2²³⁶, 84, F₂, 3, 146) (dual of [(84, 3), 16, 147]-NRT-code)	[i]
6	Linear OOA(2²³⁵, 83, F₂, 3, 145) (dual of [(83, 3), 14, 146]-NRT-code)	[i]
7	Linear OOA(2²³⁴, 83, F₂, 3, 144) (dual of [(83, 3), 15, 145]-NRT-code)	[i]
8	Linear OOA(2²³³, 83, F₂, 3, 143) (dual of [(83, 3), 16, 144]-NRT-code)	[i]
9	Linear OOA(2²³², 82, F₂, 3, 142) (dual of [(82, 3), 14, 143]-NRT-code)	[i]
10	Linear OOA(2²³¹, 82, F₂, 3, 141) (dual of [(82, 3), 15, 142]-NRT-code)	[i]
11	Linear OOA(2²³⁰, 82, F₂, 3, 140) (dual of [(82, 3), 16, 141]-NRT-code)	[i]
12	Linear OOA(2²²⁹, 81, F₂, 3, 139) (dual of [(81, 3), 14, 140]-NRT-code)	[i]
13	Linear OOA(2²²⁸, 81, F₂, 3, 138) (dual of [(81, 3), 15, 139]-NRT-code)	[i]
14	Linear OOA(2²²⁷, 81, F₂, 3, 137) (dual of [(81, 3), 16, 138]-NRT-code)	[i]
15	Linear OOA(2²²⁶, 80, F₂, 3, 136) (dual of [(80, 3), 14, 137]-NRT-code)	[i]
16	Linear OOA(2²²⁵, 80, F₂, 3, 135) (dual of [(80, 3), 15, 136]-NRT-code)	[i]
17	Linear OOA(2²²³, 79, F₂, 3, 133) (dual of [(79, 3), 14, 134]-NRT-code)	[i]
18	Linear OOA(2²²², 79, F₂, 3, 132) (dual of [(79, 3), 15, 133]-NRT-code)	[i]