Runlength limited (RLL) codes are used in magnetic recording. The error patterns that occur with peak detection magnetic recording systems when using a runlength-limited code consist of both symmetric errors and shift errors. We refer to shift errors and symmetric errors collectively as mixed type errors. A method of providing error control for mixed type errors that occur in a runlength limited code comprised of (d, k) constrained sequences is examined. The coding scheme is to choose parity blocks to insert in the constrained information sequence. The parity blocks are chosen to satisfy the constraints and to provide some error control. The cases of single error-detection and single error-correction are investigated, where the single error is allowed to be a shift error or a symmetric error. Bounds are discussed on the possible lengths for the parity blocks. It is shown that the single error-detection codes are the best possible in terms of the length of the parity blocks.

We provide useful results on two classes of convolutional codes: binary codes and nonbinary codes. The best codes or the best known codes for these two classes of convolutional codes are found, by computer search. Some of them are better than those found in the past. We specify these codes by their transfer function matrices, distance spectra, and information-weight spectra. Furthermore, we derive an upper bound on the free distances of binary-to-M-ary codes and q-ary-to-M-ary codes. Numerical values of this bound closely fit the computer-searched values.

Proposes two classes of constant weight codes, which can be used for correcting t symmetric errors and simultaneously detecting all unidirectional errors. Codes in the first class are in quasi-systematic form and codes in the second class are in systematic form. Since each codeword of codes in both classes can be divided into a data part and a parity check part, the proposed codes have the merit of easily mapping messages into codewords.>

The author investigates the (n, k, d>or=2t+1) binary linear codes, which are used for correcting error patterns of weight at most t and detecting other error patterns over a binary symmetric channel. In particular, for t=1, it is shown that there exists one code whose probability of undetected errors is upper-bounded by (n+1) (2/sup n-k/-n)/sup -1/ when used on a binary symmetric channel with transition probability less than 2/n.>

Exhaustive computation by a computer was used to find the unequal error protection capabilities of all binary cyclic codes of odd length up to 65 that have minimum distances of at least 3. For those codes for which upper bounds can only be computed on their unequal error protection capabilities, an analytic method developed by V.N. Dynkin and V.A. Togonidze (1976) is used to show that the upper bounds meet the exact unequal error protection capabilities.>

The unequal error correction capabilities of binary cyclic codes of composite length are investigated. Under certain conditions, direct sums of concatenated codes have unequal error correction capabilities. By a modified Hartmann and Tzeng (1973) algorithm, it is shown that a binary cyclic code of composite length is equivalent to the direct sum of concatenated codes. With this, some binary cyclic unequal error protection (UEP) codes are constructed. Finally, the authors present a class of two-level UEP cyclic direct-sum codes which provide error correction capabilities higher than those guaranteed by the Blokh-Zyablov (1974) constructions.>