This paper studies families of self-orthogonal codes over Z 4. We show that the simplex codes (Type α and Type β) are self-orthogonal. We partially answer the question of Z 4-linearity for the codes from projective planes of even order. A new family of self-orthogonal codes over Z 4 is constructed via projective planes of odd order. Properties such as… (More)
—In a distributed storage network, reliability and bandwidth optimization can be provided by regenerating codes. Recently table based regenerating codes viz. DRESS (Distributed Replication-based Exact Simple Storage) codes has been proposed which also optimizes the disk I/O. Dress codes consists of an outer MDS code with an inner fractional repetition (FR)… (More)
In an earlier paper the authors studied simplex codes of type α and β over Z 4 and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type α and β over Z 2 s. The generalized Gray map is then used to construct binary codes. The linear codes meet the… (More)
—In a distributed storage systems (DSS), regenerating codes are used to optimize bandwidth in the repair process of a failed node. To optimize other DSS parameters such as computation and disk I/O, Distributed Replication-based Simple Storage (Dress) Codes consisting of an inner Fractional Repetition (FR) code and an outer MDS code are commonly used. Thus… (More)
This paper studies two families of codes over Z 4 , MacDonald codes of type α and type β. The torsion code, weight distribution, and Gray image properties are studied. Some interesting optimal binary codes are also obtained. Two nonlinear families of binary codes are obtained via the Gray map.
This paper gives lower and upper bounds on the covering radius of codes over Z 2 s with respect to homogenous distance. We also determine the covering radius of various Repetition codes, Simplex codes (Type α and Type β) and their dual and give bounds on the covering radii for MacDonald codes of both types over Z 4 .
In this paper, we introduce the notions of fuzzy γ-I-open sets and fuzzy γ-I-continuous functions to obtain a decomposition of fuzzy semi-I-continuity. We also investigated the fundamental properties of such functions.
—Heterogeneous Distributed Storage Systems (DSS) are close to real world applications for data storage. Internet caching system and peer-to-peer storage clouds are the examples of such DSS. In this work, we calculate the capacity formula for such systems where each node store different number of packets and each having a different repair bandwidth (node can… (More)
—The term Big Data is usually used to describe huge amount of data that is generated by humans from digital media such as cameras, internet, phones, sensors etc. By building advanced analytics on the top of big data, one can predict many things about the user such as behavior, interest etc. However before one can use the data, one has to address many issues… (More)