MinT - Information on Result #1133196

Information on Result #1133196

Linear OOA(2²¹⁷, 690, F₂, 6, 35) (dual of [(690, 6), 3923, 36]-NRT-code), using OOA 6-folding based on linear OA(2²¹⁷, 4140, F₂, 35) (dual of [4140, 3923, 36]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹⁷, 4141, F₂, 35) (dual of [4141, 3924, 36]-code), using
- constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
  1. linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
  2. linear OA(2¹⁶⁹, 4096, F₂, 29) (dual of [4096, 3927, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  3. linear OA(2¹², 45, F₂, 5) (dual of [45, 33, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
      - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
        extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2²¹⁷, 690, F₂, 6, 34) (dual of [(690, 6), 3923, 35]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²¹⁸, 690, F₂, 6, 35) (dual of [(690, 6), 3922, 36]-NRT-code)	[i]		OOA Duplication