Abstract This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus improving existing sum-rank metric. We derive improved upper and lower based entropy distribution related to Boltzmann distribution, which work for Additionally, we closed-form specifically that outperform bounds.

Abstract New constructions for moderate-density parity-check (MDPC) codes using finite geometry are proposed. We design a matrix the main family of binary as concatenation two matrices: incidence between points and lines Desarguesian projective plane ovals bundle. A bundle is special collection which pairwise meet in unique point. determine minimum distance dimension these codes, we show that they have natural quasi-cyclic structure. consider alternative based on an compare their...

This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus improving existing sum-rank metric. We derive improved upper and lower based entropy distribution related to Boltzmann distribution, which work for Additionally, we closed-form specifically that outperform bounds.

Famous results state that the classical MacWilliams identities fail for Lee metric, homogeneous metric and subfield apart from some trivial cases. In this paper we change idea of enumerating codewords same weight choose a finer way partitioning code still contains all information enumerator code. The considered decomposition allows MacWilliams-type which hold any additive over finite chain ring. For specific cases then define coarser partition hold. This result shows one can, in fact, relate...

We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings two channels that arise from Lee metric. The first channel is a discrete memory-less (DMC) matched to second adds each codeword an error vector constant weight, where picked uniformly at random set vectors weight. It shown marginal conditional distributions coincide, in limit large block length. Random coding union bounds on probability are derived for both channels. Moreover, selected LDPC...

This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the using various novel definitions of generalized weights based on different notions a support linear code. In this regard, we introduce three main types in analyze their utility to minimum distance. Eventually, propose point view give an bound distance which discuss density maximum with respect bound.

Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes integer residue rings and analyze their performance with respect to the Lee metric. Their error-correction is studied two channel models, in The first model a discrete memoryless channel, whereas second an error vector drawn uniformly at random from all vectors of fixed weight. It known that laws coincide asymptotic regime, meaning marginal distributions...

The Lee metric syndrome decoding problem is an NP-hard and several generic decoders have been proposed. observation that such come with a larger cost than their Hamming counterparts make the promising alternative for classical code-based cryptography. Unlike in metric, error vector chosen uniform at random of given weight expected to only few entries large weight. Using this distribution entries, we are able drastically decrease by reducing original smaller instance, whose solution lives...

The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike other metrics, weight a vector may be increased or decreased by product with nonzero, nontrivial scalar. This particular interest for cryptographic applications, like example metric code-based cryptosystems, since an attacker use reduce error and thus complexity corresponding generic decoder. analyzed asymptotic regime. Furthermore, construction constant using integer partitions efficient method...

We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings two channels that arise from Lee metric. The first channel is a discrete memory-less (DMC) matched to second adds each codeword an error vector constant weight, where picked uniformly at random set vectors weight. It shown marginal conditional distributions coincide, in limit large block length. Random coding union bounds on probability are derived for both channels. Moreover, selected LDPC...

A new construction for moderate density parity-check (MDPC) codes using finite geometry is proposed. We design a matrix this family of binary as the concatenation two matrices: incidence between points and lines Desarguesian projective plane ovals bundle. bundle special collection which pairwise meet in unique point. determine minimum distance dimension these codes, showing that they have natural quasi-cyclic structure. In addition, we analyze error-correction performance within one round...