Abstract: Error correction for polynomial block codes is achieved without prior evaluation of power sum symmetric functions. The received word R (z) is reduced mod G (z), the generator of the code and a function F (z) of error locator polynomial W(z), errata values Y and code dependent functions f(x.sub.i) of the error positions x.sub.i given by ##EQU1## is decomposed into a rational polynomial function N (z)/W (z) for which deg (N (z) )<deg ( W (z) )<number of correctable errors. W (z) is the error locator polynomial, the roots of which are the errata locations X and Y, the correction to the received character is obtained from ##EQU2## evaluated at X.sub.i using non-erased check symbols of R (z). Correction is carried out in a crossbar switch structure which recalls a stored copy of R (z) and corrects bits as specified by (X.sub.i, Y.sub.i).

Abstract: To each bit time of a data block, there is associated a counter which is incremented or decremented in accord with the congruence or non-congruence of the c bit sequence associated with the respective counter (for example, the first bit of the c bit sequence). The counters are initialized to an optimum non-zero value and after receiving a number of blocks of data, each containing one sync symbol, the synchronization is determined from the relative content of the counters.

Abstract: An encoder for Reed Solomon codes employs structure for producing interleaved code wherein redundancy bits are realized by a bit serial multiplicative procedure. Operations are accomplished with respect to the dual basis to the conventional polynomial representational basis as coefficients of successive powers of an element of a finite field. Code bits are generated and interleaved by a feedback shift register constructed from standard RAM chips. The structure is simplified by selection of a generator polynomial from a class which exhibits symmetry whereby the number of independent coefficients for representing the generator polynomial is halved.

Abstract: A saddle coil for operation in the probe of an NMR spectrometer is formed from coil portions of opposite helicities disposed on a flexible insulating material, the outer windings of said portions connected by a linking conductor disposed on said insulating medium, which medium is then deformed to form a cylindrical body.

Abstract: An improved technique is disclosed for forming two- or three-dimensional images of a macroscopic sample by means of gyromagnetic resonance. A train of free induction decay transient resonance signals are induced and detected from a sample in a region to be imaged. A sequence of pulsed magnetic field gradients are applied during the series of free induction decay signals to derive sets of gyromagnetic resonance data as a function of the changing magnetic field gradients. Two- or three-dimensional images are reconstructed from the sets of resonance data by two- or three-dimensional Fourier transformation.