Golay and other box codes

The (24,12;8) extended Golay Code can be generated as a 6 x 4 binary matrix from the (15,11;3) BCH-Hamming Code, represented as a 5 x 3 matrix, by adding a row and a column, both of odd or even parity. The odd-parity case provides the additional 12th dimension. Furthermore, any three columns and five rows of the 6 x 4 Golay form a BCH-Hamming (15,11;3) Code. Similarly a (80,58;8) code can be generated as a 10 x 8 binary matrix from the (63,57;3) BCH-Hamming Code represented as a 9 x 7 matrix by adding a row and a column both of odd and even parity. Furthermore, any seven columns along with the top nine rows is a BCH-Hamming (53,57;3) Code. A (80,40;16) 10 x 8 matrix binary code with weight structure identical to the extended (80,40;16) Quadratic Residue Code is generated from a (63,39;7) binary cyclic code represented as a 9 x 7 matrix, by adding a row and a column, both of odd or even parity

Nonlinear, nonbinary cyclic group codes

New cyclic group codes of length 2(exp m) - 1 over (m - j)-bit symbols are introduced. These codes can be systematically encoded and decoded algebraically. The code rates are very close to Reed-Solomon (RS) codes and are much better than Bose-Chaudhuri-Hocquenghem (BCH) codes (a former alternative). The binary (m - j)-tuples are identified with a subgroup of the binary m-tuples which represents the field GF(2 exp m). Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. For low rates, a second shift-register encoding operation may be invoked. Decoding uses the RS error-correcting procedures for the m-tuple codes for m = 4, 5, and 6

A (72, 36; 15) box code

A (72,36;15) box code is constructed as a 9 x 8 matrix whose columns add to form an extended BCH-Hamming (8,4;4) code and whose rows sum to odd or even parity. The newly constructed code, due to its matrix form, is easily decodable for all seven-error and many eight-error patterns. The code comes from a slight modification in the parity (eighth) dimension of the Reed-Solomon (8,4;5) code over GF(512). Error correction uses the row sum parity information to detect errors, which then become erasures in a Reed-Solomon correction algorithm

Soft decoding a self-dual (48, 24; 12) code

A self-dual (48,24;12) code comes from restricting a binary cyclic (63,18;36) code to a 6 x 7 matrix, adding an eighth all-zero column, and then adjoining six dimensions to this extended 6 x 8 matrix. These six dimensions are generated by linear combinations of row permutations of a 6 x 8 matrix of weight 12, whose sums of rows and columns add to one. A soft decoding using these properties and approximating maximum likelihood is presented here. This is preliminary to a possible soft decoding of the box (72,36;15) code that promises a 7.7-dB theoretical coding under maximum likelihood

More box codes

A new investigation shows that, starting from the BCH (21,15;3) code represented as a 7 x 3 matrix and adding a row and column to add even parity, one obtains an 8 x 4 matrix (32,15;8) code. An additional dimension is obtained by specifying odd parity on the rows and even parity on the columns, i.e., adjoining to the 8 x 4 matrix, the matrix, which is zero except for the fourth column (of all ones). Furthermore, any seven rows and three columns will form the BCH (21,15;3) code. This box code has the same weight structure as the quadratic residue and BCH codes of the same dimensions. Whether there exists an algebraic isomorphism to either code is as yet unknown

Ultrastructural alteration of mouse lung by prolonged exposure to mixtures of helium and oxygen

Observed changes consist mainly of blebbing of capillary endothelium and alveolar epithelium, which is quite possibly indicative of cellular edema; also, there can be observed highly-convoluted basement membrane, alveolar debris, and increased numbers of platelets

A robust high-sensitivity algorithm for automated detection of proteins in two-dimensional electrophoresis gels

The automated interpretation of two-dimensional gel electrophoresis images used in protein separation and analysis presents a formidable problem in the detection and characterization of ill-defined spatial objects. We describe in this paper a hierarchical algorithm that provides a robust, high-sensitivity solution to this problem, which can be easily adapted to a variety of experimental situations. The software implementation of this algorithm functions as part of a complete package designed for general protein gel analysis applications

Dissipative "Groups" and the Bloch Ball

We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball.Comment: 4 pages. Proceedings of Group 24, Paris, July, 200

Dissipative Quantum Control

Nature, in the form of dissipation, inevitably intervenes in our efforts to control a quantum system. In this talk we show that although we cannot, in general, compensate for dissipation by coherent control of the system, such effects are not always counterproductive; for example, the transformation from a thermal (mixed) state to a cold condensed (pure state) can only be achieved by non-unitary effects such as population and phase relaxation.Comment: Contribution to Proceedings of \emph{ICCSUR 8} held in Puebla, Mexico, July 2003, based on talk presented by Allan Solomon (ca 8 pages, latex, 1 latex figure, 2 pdf figures converted to eps, appear to cause some trouble