We demonstrate a majority-logic decoding algorithm for decoding the generalised hyperoctahedral group Cm wr Sn when thought of as an error-correcting code. We also find the complexity of this decoding algorithm and compare it with that of another, more general, algorithm. Finally, we enumerate the number of error patterns exceeding the correction capability that can be successfully decoded by t...

the problem of series two-block disjoint decomposition of completely specifiedboolean functions is considered. analysis and investigation of such systems are veryimportant in logical design context. recently, a good method for solving thisproblem was suggested which has been based on the ternary matrix cover approach.using this method a computer program was developed. this paper is focused onde...

Multinomial representations are derived for majority logic operations on bipolar binary data. The coefficients are given simply in terms of the readily computed lower Cholesky factor of Pascal Matrices of order n for codes of block length n. Sufficient conditions on majority logic codes having no deterministic errors introduced in the majority logic coding and majority logic decoding process ar...

As an emerging technology, Quantum-dot Cellular Automata (QCA) has been extensively analyzed in the technical literature for implementing logic circuits; in this technology, the basic combinational circuit is the majority voter with three inputs. In this paper, the design of a logic gate which implements any combinational function of at most three input variables is presented. This type of gate...

We study the extension of dependence logic D by a majority quantifier M over finite structures. Dependence logic [19] extends first-order logic by dependence atomic formulas =(t1, . . . , tn) the intuitive meaning of which is that the value of the term tn is completely determined by the values of t1, . . . , tn−1. While in first-order logic the order of quantifiers solely determines the depende...

In-memory computing using emerging technologies such as resistive random-access memory (ReRAM) addresses the ‘von Neumann bottleneck’ and strengthens present research impetus to overcome wall. While many methods have been recently proposed implement Boolean logic in memory, latency of arithmetic circuits (adders consequently multipliers) implemented a sequence operations increases greatly with ...

Majority-logic decoding is attractive for three reasons: (I) It can be simply implemented; (2 ) the decoding delay is short; and (3) its performance, while suboptimal, is always superior to bounded distance decoding. For these reasons, majoritylogic decodable cyclic codes are very suitable f o r error control in high speed digital data transmission systems. Among the majority-logic decodable co...

As a new paradigm for nanoscale technologies, approximate computing deals with error tolerance in the computational process to improve performance and reduce power consumption. Majority logic (ML) is applicable many emerging nanotechnologies; its basic building block (the 3-input majority voter, MV) has been extensively used digital circuit design. In this paper, designs of adders multipliers b...