MinT - Information on Result #1131174

Information on Result #1131174

Linear OOA(2¹³⁶, 87385, F₂, 6, 15) (dual of [(87385, 6), 524174, 16]-NRT-code), using OOA 6-folding based on linear OA(2¹³⁶, 524310, F₂, 15) (dual of [524310, 524174, 16]-code), using

1 times code embedding in larger space [i] based on linear OA(2¹³⁵, 524309, F₂, 15) (dual of [524309, 524174, 16]-code), using
- constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
  1. linear OA(2¹³⁴, 524288, F₂, 15) (dual of [524288, 524154, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  2. linear OA(2¹¹⁵, 524288, F₂, 13) (dual of [524288, 524173, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(2¹³⁷, 87385, F₂, 6, 15) (dual of [(87385, 6), 524173, 16]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹³⁸, 87385, F₂, 6, 15) (dual of [(87385, 6), 524172, 16]-NRT-code)	[i]
3	Linear OOA(2¹³⁹, 87385, F₂, 6, 15) (dual of [(87385, 6), 524171, 16]-NRT-code)	[i]