Binary MDS linear codes are well-known. We prove that any binary MDS systematic non-linear code is equivalent to a linear code and hence we classify them completely.

High frequency design and instruction-level parallelism (ILP) are two keys to high performance microprocessor implementation. To achieve these sometimes competing goals, the Binary-translation Optimized Architecture (BOA) aims to bring code translation techniques based on continuous profiling into the mainstream. Initially, code is interpreted to detect code hot spots and gather profile informa...

The probability that a complete binary prefix code has a selfsynchronizing string approaches one, as the number of codewords tends to infinity.

A cyclically permutable code is a binary code whose codewords are cyclically distinct and have full cyclic order. An important class of these codes are the constant weight cyclically permutable codes. In a code of this class all codewords have the same weight w. These codes have many applications, including in optical code-division multiple-access communication systems and in constructing proto...

Our purpose is to find an upper bound for the length of s-extremal codes over F2 (resp. F4) when d ≡ 2 (mod 4) (resp. d odd). This question is left open in [6], [2]. More precisely, we show that there is no s-extremal binary code of length n ≥ 21d− 82 if d > 6 and d ≡ 2 (mod 4). Similarly we show that there is no s-extremal additive F4 code of length n ≥ 13d− 26 if d > 1 and d is odd. We also d...

In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. In particular, we present a procedure to recover bursts of erasures that are distributed in a diagonal line. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main...

An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Qn such that every vector x ∈ Qn can be obtained from some vector c ∈ C by changing at most R 1’s of c to 0’s, where R is as small as possible. K(n,R) is defined as the smallest size of such a code. We show K(n,R) ∈ Θ(2/n) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. W...

A general decoding method for cyclic codes is presented which gives promise of substantially reducing the complexity of decoders at the cost of a modest increase in decoding time (or delay). Significant reductions in decoder complexity for binary cyclic finite-geometry codes are demonstrated, and two decoding options for the Golay code are presented.

An (n, d, k)-mapping f is a mapping from binary vectors of length n to permutations of length n + k such that for all x, y ∈ {0, 1}n , dH ( f (x), f (y)) ≥ dH (x, y) + d , if dH (x, y) ≤ (n+k)−d and dH ( f (x), f (y)) = n+k, if dH (x, y) > (n+k)−d . In this paper, we construct an (n, 3, 2)-mapping for any positive integer n ≥ 6. An (n, r)-permutation array is a permutation array of length n and...

Bose-Chaudhuri-Hocquenghem and Justesen codes are used to pack equa spheres in M-dimensional Euclidean space with density A satisfying log2 A > — 6n + o(ri), for all sufficiently large n of the form m2, where m is a power of 4. These appear to be the densest packings yet constructed in high dimensional space.