In this paper, we investigate how to obtain binary locally repairable codes (LRCs) with good locality and availability from binary Simplex codes. We first propose a Combination code having the generator matrix with all the columns of positive weights less than or equal to a given value. Such a code can be also obtained by puncturing all the columns of weights larger than a given value from a binary Simplex Code. We call by block-puncturing such puncturing method. Furthermore, we suggest a heuristic puncturing method, called subblock-puncturing, that punctures a few more columns of the largest weight from the Combination code. We determine the minimum distance, locality, availability, joint information locality, joint information availability of Combination codes in closed-form. We also demonstrate the optimality of the proposed codes with certain choices of parameters in terms of some well-known bounds.
|Number of pages||8|
|Journal||IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences|
|Publication status||Published - 2018 Dec|
Bibliographical noteFunding Information:
Manuscript received January 6, 2018. Manuscript revised July 24, 2018. †The author is with Samsung Electronics, Seoul, Korea. ††The authors are with Yonsei University, Seoul, Korea. ∗He had contributed to this work while he had been with Yonsei University, Seoul, Korea. ∗∗This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B4011191). a) E-mail: firstname.lastname@example.org b) E-mail: email@example.com c) E-mail: firstname.lastname@example.org (Corresponding author) DOI: 10.1587/transfun.E101.A.2374
Copyright © 2018 The Institute of Electronics, Information and Communication Engineers.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics