MinT - Information on Result #1052180

Information on Result #1052180

Linear OOA(2²⁴⁴, 2097278, F₂, 4, 18) (dual of [(2097278, 4), 8388868, 19]-NRT-code), using OOA 2-folding based on linear OOA(2²⁴⁴, 4194556, F₂, 2, 18) (dual of [(4194556, 2), 8388868, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁴, 4194557, F₂, 2, 18) (dual of [(4194557, 2), 8388870, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³⁷, 256, F₂, 2, 9) (dual of [(256, 2), 475, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2³⁷, 512, F₂, 9) (dual of [512, 475, 10]-code), using
      - an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  2. linear OOA(2²⁰⁷, 4194301, F₂, 2, 18) (dual of [(4194301, 2), 8388395, 19]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2²⁰⁷, 8388602, F₂, 18) (dual of [8388602, 8388395, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and 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		Method
1	Linear OOA(2²⁴⁴, 2045875, F₂, 5, 18) (dual of [(2045875, 5), 10229131, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴⁴, 2045875, F₂, 6, 18) (dual of [(2045875, 6), 12275006, 19]-NRT-code)	[i]
3	Linear OOA(2²⁴⁴, 2045875, F₂, 7, 18) (dual of [(2045875, 7), 14320881, 19]-NRT-code)	[i]
4	Linear OOA(2²⁴⁴, 2045875, F₂, 8, 18) (dual of [(2045875, 8), 16366756, 19]-NRT-code)	[i]
5	Digital (226, 244, 2045875)-net over F₂	[i]