MinT - Information on Result #1686135

Information on Result #1686135

Linear OOA(2²¹⁴, 3109432, F₂, 7, 14) (dual of [(3109432, 7), 21765810, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁴, 3109432, F₂, 2, 14) (dual of [(3109432, 2), 6218650, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹⁴, 4325372, F₂, 2, 14) (dual of [(4325372, 2), 8650530, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵³, 131071, F₂, 2, 7) (dual of [(131071, 2), 262089, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (46, 53, 131071)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2²¹⁴, 3109431, F₂, 8, 14) (dual of [(3109431, 8), 24875234, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2²¹⁴, 3109431, F₂, 21, 14) (dual of [(3109431, 21), 65297837, 15]-NRT-code)	[i]		OOA Stacking with Additional Row