MinT - Information on Result #1133487

Information on Result #1133487

Linear OOA(2²⁴¹, 690, F₂, 6, 39) (dual of [(690, 6), 3899, 40]-NRT-code), using OOA 6-folding based on linear OA(2²⁴¹, 4140, F₂, 39) (dual of [4140, 3899, 40]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁴¹, 4141, F₂, 39) (dual of [4141, 3900, 40]-code), using
- constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
  1. linear OA(2²²⁹, 4096, F₂, 39) (dual of [4096, 3867, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
  2. linear OA(2¹⁹³, 4096, F₂, 33) (dual of [4096, 3903, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [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(2²⁴¹, 690, F₂, 6, 38) (dual of [(690, 6), 3899, 39]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁴², 690, F₂, 6, 39) (dual of [(690, 6), 3898, 40]-NRT-code)	[i]		OOA Duplication