Ang Miin Huey

Bio: Ang Miin Huey is an academic researcher from Universiti Sains Malaysia. The author has contributed to research in topics: Hamming(7,4) & Multidimensional parity-check code. The author has an hindex of 2, co-authored 3 publications receiving 46 citations.

On parikh matrices

Abstract: Mateescu et al (2000) introduced an interesting new tool, called Parikh matrix, to study in terms of subwords, the numerical properties of words over an alphabet. The Parikh matrix gives more information than the well-known Parikh vector of a word which counts only occurrences of symbols in a word. In this note a property of two words u, υ, called "ratio property", is introduced. This property is a sufficient condition for the words uυ and υu to have the same Parikh matrix. Thus the ratio property gives information on the M–ambiguity of certain words and certain sets of words. In fact certain regular, context-free and context-sensitive languages that have the same set of Parikh matrices are exhibited. In the study of fair words, Cerny (2006) introduced another kind of matrix, called the p–matrix of a word. Here a "weak-ratio property" of two words u, υ is introduced. This property is a sufficient condition for the words uυ and υu to have the same p–matrix. Also the words uυ and υu are fair whenever u, υ are fair and have the weak ratio property.

Efficient Algorithms for Reconstruction of 2D-Arrays from Extended Parikh Images

Abstract: The concept of a Parikh matrix or an extended Parikh mapping of words introduced by Mateescu et al (2001) is formulated here for two-dimensional (2D) arrays. A polynomial time algorithm is proposed to reconstruct an unknown 2D-array over { 0,1 } from its image under the extended Parikh mapping along a single direction. On the other hand the problem of reconstructing a 2D-array over { 0,1 } from its image under the extended Parikh mapping along three or more directions is shown to be NP-hard. Also a polynomial time algorithm to reconstruct a 2D-array over {0,1} with a maximum number of ones close to the main diagonal of the array is presented by reducing the problem to Min-cost Max-flow problem.

The Check Positions of Hamming Codes and the Construction of a 2 EC-AUED Code

Abstract: Hamming Code is the oldest and the most commonly used single error correcting and double errors detecting code. For implication, it is constructed over the field . For each , there is a Hamming Code where and . A message word of length k is encoded using a generating matrix G into a codeword of length n. This amounts to inserting r parity check digits into the message word. The positions of the parity check digits in the codeword are called the check positions of the code (with respect to G). A received word is then decoded using a parity check matrix H. If the check positions of the code are in the coordinates of the codeword, then the rows of H are called the check rows of the code. We proved in this paper that for any parity check matrix of a Hamming Code, there exists a generating matrix G of the code, such that the check rows of the code are linearly independent. We believe that this fact is contained implicitly in a paper of Hamming (7) but we cannot find any explicit proof in existing literature. Using the above fact, we construct a 2 ) 2 ( GF 2 ≥ r ) 3 , , ( k n 1 2 − = r n 1 2 − − = r k r th th 2 th 1 , , , r i i i " th th 2 th 1 , , , r i i i "

On Core Words and the Parikh Matrix Mapping

Abstract: Core of a binary word, recently introduced, is a refined way to characterize binary words having the same Parikh matrices, as well as bridging the connection between binary words and partitions of natural numbers. This paper continues the work by generalizing to higher alphabet. The core of a word as well as the relatived version is the essential part of a word that captures the key information of the word from the perspective of its Parikh matrix. Various nice properties of the cores and some interesting results regarding the M-equivalence classes of ternary words are obtained.

Subword occurrences, parikh matrices and lyndon images

Abstract: We investigate the number of occurrences of a word u as a (scattered) subword of a word w. The notion of a Parikh matrix, recently introduced, is a basic tool in this investigation. In general, sev...

Product of parikh matrices and commutativity

Abstract: The Parikh vector of a word enumerates the symbols of the alphabet that occur in the word. The Parikh matrix of a word which has been recently introduced, is an extension of the notion of Parikh vector and gives more numerical information about the word in terms of certain subwords. Intensive investigation on various theoretical properties of Parikh matrices has taken place. This paper deals with the problem of finding properties of words so that their Parikh matrices commute.