Based on the notion of an order function we construct and determine the parameters of a class of error-correcting evaluation codes. This class includes the one-point algebraic geometry codes as well as the generalized Reed-Muller codes, and the parameters are determined without using heavy machinery from algebraic geometry.

An algorithm for finding the unequal error protection (UEP) capability of a q-ary image of a low-rate qm-ary cyclic code is presented by combining its concatenated structure with the UEP capability of concatenated codes. The results are independent of a choice of a basis to be used for expanding an element over GF(qm) into GF(q). A table of the UEP capability of binary images of low-rate Reed-S...

Forward error correction codes (FEC) are used for error detection and correction in communication systems. Low density parity check code (LDPC) is used as a powerful Forward Error Correction code in long distance communication systems which works close to the Shannon limit. Unlike other conventional channel code, the decoding algorithm used for LDPC codes is an iterative message passing algorit...

As technology scales, VLSI performance has experienced an exponential growth. As feature sizes shrink, however, we will face new challenges such as soft errors (single-event upsets) to maintain the reliability of circuits. Recent studies have tried to address soft errors with error detection and correction techniques such as error correcting codes and redundant execution. However, these techniq...

For discrete memoryless multiple-access channels, we propose a general definition of variable length codes with a measure of the transmission rates at the receiver side. This gives a receiver perspective on the multiple-access channel coding problem and allows us to characterize the region of achievable rates when the receiver is able to decode each transmitted message at a different instant of...

Recently [1] we proposed a family of magic state distillation protocols that obtains asymptotic performance that is conjectured to be optimal. This family depends upon several codes, called “inner codes” and “outer codes.” In Ref. [1], some small examples of these codes were given as well as an analysis of codes in the asymptotic limit. Here, we analyze such protocols in an intermediate size re...

Baranyai’s theorem is a well-known theorem in the theory of hypergraphs. A corollary of this theorem says that one can partition the family of all u-subsets of an n-element set into ( n−1 u−1 ) sub-families such that each sub-family form a partition of the n-element set, where n is divisible by u. In this paper, we present a codingtheoretic application of Baranyai’s theorem (or equivalently, th...

Physical Unclonable Functions can be used for secure key generation in cryptographic applications. It is explained how methods from coding theory must be applied in order to ensure reliable key regeneration. Based on previous work, we show ways how to obtain better results with respect to error probability and codeword length. Also, an example based on Generalized Concatenated codes is given, w...

The unequal error correction capabilities of binary cyclic codes of composite length aye investigated. Under certain conditions, direct sums of concatenated codes have unequal error correction capabilities. By a modified Hartmann and Tzeng 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 une...

We describe a concatenated coding system with iterated sequential inner decoding. The system uses convolutional codes of very long constraint length and operates on iterations between an inner Fano decoder and an outer Reed-Solomon decoder.