MinT - Information on Result #1095905

Information on Result #1095905

Linear OOA(2¹⁷⁴, 104862, F₂, 5, 19) (dual of [(104862, 5), 524136, 20]-NRT-code), using OOA 5-folding based on linear OA(2¹⁷⁴, 524310, F₂, 19) (dual of [524310, 524136, 20]-code), using

1 times code embedding in larger space [i] based on linear OA(2¹⁷³, 524309, F₂, 19) (dual of [524309, 524136, 20]-code), using
- constructionÂ X4 applied to C_e(18) âŠ‚ C_e(16) [i] based on
  1. linear OA(2¹⁷², 524288, F₂, 19) (dual of [524288, 524116, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(2¹⁵³, 524288, F₂, 17) (dual of [524288, 524135, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
    - strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
      - dual of repetition code with length 21 [i]
  4. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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		Method
1	Linear OOA(2¹⁷⁵, 104862, F₂, 5, 19) (dual of [(104862, 5), 524135, 20]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁷⁶, 104862, F₂, 5, 19) (dual of [(104862, 5), 524134, 20]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁷, 104862, F₂, 5, 19) (dual of [(104862, 5), 524133, 20]-NRT-code)	[i]