MinT - Information on Result #1152612

Information on Result #1152612

Linear OOA(2²⁵¹, 2348, F₂, 7, 34) (dual of [(2348, 7), 16185, 35]-NRT-code), using OOA 7-folding based on linear OA(2²⁵¹, 16436, F₂, 34) (dual of [16436, 16185, 35]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁵¹, 16438, F₂, 34) (dual of [16438, 16187, 35]-code), using
- 1 times truncation [i] based on linear OA(2²⁵², 16439, F₂, 35) (dual of [16439, 16187, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
    1. linear OA(2²³⁹, 16384, F₂, 35) (dual of [16384, 16145, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(2¹⁹⁷, 16384, F₂, 29) (dual of [16384, 16187, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(2¹³, 55, F₂, 5) (dual of [55, 42, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(2²⁵³, 2348, F₂, 7, 34) (dual of [(2348, 7), 16183, 35]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁵⁴, 2348, F₂, 7, 34) (dual of [(2348, 7), 16182, 35]-NRT-code)	[i]		OOA Duplication