Constructions of optimal locally repairable codes over small fields
نویسندگان
چکیده
منابع مشابه
Optimal locally repairable codes via elliptic curves
Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg [14] first gave a breakthrough result in this topic by cleverly considering subcodes of Reed-Solomon codes. Thus, q-ary optimal locally repairable codes from subcodes of Reed-Solomon codes giv...
متن کاملConstructions of optimal LCD codes over large finite fields
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis.
متن کاملConstructions of High-Rate MSR Codes over Small Fields
Three constructions of minimum storage regenerating (MSR) codes are presented. The first two constructions provide access-optimal MSR codes, with two and three parities, respectively, which attain the sub-packetization bound for access-optimal codes. The third construction provides larger MSR codes with three parities, which are not access-optimal, and do not necessarily attain the sub-packetiz...
متن کاملLocally Repairable Regenerating Code Constructions
In this work, we give locally repairable regenerating code (LRRC) [1]–[4] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the minimum-bandwidthregenerating (MBR) point. I. RANDOM LINEAR CODE CONSTRUCTION FOR A CLASS OF (n, k, d, r) PARAMETERS In this section, we prove the existence and construction of linea...
متن کاملConstruction of optimal locally repairable codes via automorphism groups of rational function fields
Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. In this paper, an optimal locally repairable code refers to a block code achieving this Singleton-type bound. Like classical MDS co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2017
ISSN: 1674-7216
DOI: 10.1360/n012016-00206