Cyclic code

About: Cyclic code is a research topic. Over the lifetime, 3755 publications have been published within this topic receiving 63255 citations.

Fixed content distributed data storage using permutation ring encoding

Abstract: A file protection scheme for fixed content in a distributed data archive uses computations that leverage permutation operators of a cyclic code. In an illustrative embodiment, an N+K coding technique is described for use to protect data that is being distributed in a redundant array of independent nodes (RAIN). The data itself may be of any type, and it may also include system metadata. According to the invention, the data to be distributed is encoded by a dispersal operation that uses a group of permutation ring operators. In a preferred embodiment, the dispersal operation is carried out using a matrix of the form [I N — C] where I N is an n×n identity sub-matrix and C is a k×n sub-matrix of code blocks. The identity sub-matrix is used to preserve the data blocks intact. The sub-matrix C preferably comprises a set of permutation ring operators that are used to generate the code blocks. The operators are preferably superpositions that are selected from a group ring of a permutation group with base ring Z 2 .

Nonrandom binary superimposed codes

Abstract: A binary superimposed code consists of a set of code words whose digit-by-digit Boolean sums (1 + 1 = 1) enjoy a prescribed level of distinguishability. These codes find their main application in the representation of document attributes within an information retrieval system, but might also be used as a basis for channel assignments to relieve congestion in crowded communications bands. In this paper some basic properties of nonrandom codes of this family are presented, and formulas and bounds relating the principal code parameters are derived. Finally, there are described several such code families based upon (1) q -nary conventional error-correcting codes, (2) combinatorial arrangements, such as block designs and Latin squares, (3) a graphical construction, and (4) the parity-check matrices of standard binary error-correcting codes.

Generalized Hamming weights for linear codes

Abstract: Motivated by cryptographical applications, the algebraic structure, of linear codes from a new perspective is studied. By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained. These weights characterize the code performance on the wire-tap channel of type II. Basic properties of generalized weights are derived, the values of these weights for well-known classes of codes are determined, and lower bounds on code parameters are obtained. Several open problems are also listed. >

A DC-balanced, partitioned-block, 8B/10B transmission code

Abstract: This paperd escribes a byte-oriented binary transmission code and its implementation. This code is particularly well suited for high-speed local area networks and similar data links, where the information format consists of packets, variable in length, from about a dozen up to several hundred 8-bit bytes. The proposed transmission code translates each source byte into a constrained 10-bit binary sequence which hase excellent performance parameters near the theoretical limits for 8B/10B codes. The maximum run length is 5 and the maximum digital sum variation is 6. A single error in the encoded bits can, at most, generate an error burst of length 5 in the decoded domain. A very simple implementation of the code has been accomplished by partitioning the coder into 5B/6B and 3B/4B subordinate coders.

A class of optimal minimum odd-weight-column SEC-DED codes

Abstract: The class of codes described in this paper is used for single-error correction and double-error detection (SEC-DED). It is equivalent to the Hamming SEC-DED code in the sense that for a specified number k of data bits, the same number of check bits r is used. The minimum odd-weight-column code is suitable for applications to computer memories or parallel systems. A computation indicates that this code is better in performance, cost and reliability than are conventional Hamming SEC-DED codes.