MinT - Information on Result #2457988

Information on Result #2457988

Linear OOA(2¹⁵², 84, F₂, 2, 81) (dual of [(84, 2), 16, 82]-NRT-code), using 2 step truncation based on linear OOA(2¹⁵⁴, 85, F₂, 2, 83) (dual of [(85, 2), 16, 84]-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(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(2¹⁵⁶, 86, F₂, 2, 81) (dual of [(86, 2), 16, 82]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁵⁸, 87, F₂, 2, 81) (dual of [(87, 2), 16, 82]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁰, 88, F₂, 2, 81) (dual of [(88, 2), 16, 82]-NRT-code)	[i]
4	Linear OOA(2¹⁶², 89, F₂, 2, 81) (dual of [(89, 2), 16, 82]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁴, 90, F₂, 2, 81) (dual of [(90, 2), 16, 82]-NRT-code)	[i]
6	Linear OOA(2¹⁵², 42, F₂, 4, 81) (dual of [(42, 4), 16, 82]-NRT-code)	[i]	OOA Folding