For locally repairable codes (LRCs), V. Cadambe and A. Mazumdar derived the first field-dependent parameter bound, known as the C-M bound. However, the C-M bound depends on an undetermined parameter k(q)opt(n; d). In this paper,a sphere-packing approach is developed for upper bounding the parameter k for [n; k; d] linear LRCs with locality r. When restricted to the binary field, three upper bounds (i.e., Bound A, Bound B, and Bound C) are derived in explicit form. More specifically, Bound A holds under the hypothesis that the local repair groups are disjoint and of equal size. Comparing with previous bounds obtained under the same hypothesis, Bound A either covers them as special cases or has an advantage due to its explicit form. Then the hypothesis is removed in Bound B and Bound C. As the price for explicit form, Bound B specially holds for d 5 and Bound C for r = 2. Through specific comparisons we show that Bound B and Bound C both tend to out perform the C-M bound as n goes large. Moreover, a family of binary linear LRCs with d 6 attaining Bound B is constructed and later extended to a wider range of parameters by a shortening technique. Lastly, most of the bounds and constructions are extended to q-ary LRCs.
To View the Base Paper Abstract Contents
Now it is Your Time to Shine.
Great careers Start Here.
We Guide you to Every Step
Success! You're Awesome
Thank you for filling out your information!
We’ve sent you an email with your Final Year Project PPT file download link at the email address you provided. Please enjoy, and let us know if there’s anything else we can help you with.
To know more details Call 900 31 31 555
The WISEN Team