MinT - Information on Result #1631646

Information on Result #1631646

Linear OOA(2¹²¹, 2491594, F₂, 5, 10) (dual of [(2491594, 5), 12457849, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²¹, 2491594, F₂, 3, 10) (dual of [(2491594, 3), 7474661, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹²¹, 2796206, F₂, 3, 10) (dual of [(2796206, 3), 8388497, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶, 5, F₂, 3, 5) (dual of [(5, 3), 9, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹¹⁵, 2796201, F₂, 3, 10) (dual of [(2796201, 3), 8388488, 11]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹¹⁵, large, F₂, 10) (dual of [large, large−115, 11]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹²¹, 2491593, F₂, 6, 10) (dual of [(2491593, 6), 14949437, 11]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹²¹, 2491593, F₂, 7, 10) (dual of [(2491593, 7), 17441030, 11]-NRT-code)	[i]
3	Linear OOA(2¹²¹, 2491593, F₂, 8, 10) (dual of [(2491593, 8), 19932623, 11]-NRT-code)	[i]
4	Linear OOA(2¹²¹, 2491593, F₂, 15, 10) (dual of [(2491593, 15), 37373774, 11]-NRT-code)	[i]