MinT - Information on Result #1143453

Information on Result #1143453

Linear OOA(2²⁵⁰, 4194306, F₂, 6, 12) (dual of [(4194306, 6), 25165586, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷, 5, F₂, 6, 6) (dual of [(5, 6), 23, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁷, 5, F₂, 5, 6) (dual of [(5, 5), 18, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,18P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2²⁴³, 4194301, F₂, 6, 12) (dual of [(4194301, 6), 25165563, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2²⁴³, 8388602, F₂, 3, 12) (dual of [(8388602, 3), 25165563, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2²⁴³, large, F₂, 3, 12), using
    - trace code [i] based on linear OOA(8⁸¹, 2796201, F₈, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(8⁸¹, large, F₈, 12) (dual of [large, large−81, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁰, 4194305, F₂, 7, 12) (dual of [(4194305, 7), 29359885, 13]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(2²⁵⁰, 4194305, F₂, 8, 12) (dual of [(4194305, 8), 33554190, 13]-NRT-code)	[i]
3	Linear OOA(2²⁵⁰, 4194305, F₂, 18, 12) (dual of [(4194305, 18), 75497240, 13]-NRT-code)	[i]