MinT - Information on Result #1670737

Information on Result #1670737

Linear OOA(2²³⁹, 2031, F₂, 6, 37) (dual of [(2031, 6), 11947, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁹, 2031, F₂, 4, 37) (dual of [(2031, 4), 7885, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁹, 2052, F₂, 4, 37) (dual of [(2052, 4), 7969, 38]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²³⁸, 2052, F₂, 4, 37) (dual of [(2052, 4), 7970, 38]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2²³⁸, 8208, F₂, 37) (dual of [8208, 7970, 38]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2²³⁶, 8206, F₂, 37) (dual of [8206, 7970, 38]-code), using
      - constructionÂ X applied to C_e(36) âŠ‚ C_e(34) [i] based on
        linear OA(2²³⁵, 8192, F₂, 37) (dual of [8192, 7957, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
        linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
        linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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: 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(2²³⁹, 676, F₂, 42, 37) (dual of [(676, 42), 28153, 38]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row