MinT - Information on Result #1084640

Information on Result #1084640

Linear OOA(3²³³, 4194307, F₃, 4, 16) (dual of [(4194307, 4), 16776995, 17]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁷⁶, 2097150, F₃, 4, 8) (dual of [(2097150, 4), 8388524, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁵¹, 2097150, F₃, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²³³, 2097153, F₃, 20, 16) (dual of [(2097153, 20), 41942827, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row