相关论文: Codes Satisfying the Chain Condition with a Poset …
We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotient of polygonal lattices, such edge labellings descend to the…
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…
We make a detailed analysis on validity of gauge-fixing conditions and the structure of propagators in the Wess-Zumino-Witten-type open superstring field theory. First, we generalize the gauge-fixing conditions considered in JHEP 03 (2012)…
Given complex numbers $w_1, \ldots, w_n$, we define the weight $w(X)$ of a set $X$ of 0-1 vectors as the sum of $w_1^{x_1} \cdots w_n^{x_n}$ over all vectors $(x_1, \ldots, x_n)$ in $X$. We present an algorithm, which for a set $X$ defined…
Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.
A binary poset code of codimension M (of cardinality 2^{N-M}, where N is the code length) can correct maximum M errors. All possible poset metrics that allow codes of codimension M to be M-, (M-1)- or (M-2)-perfect are described. Some…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
Let $(\mathcal{P},\leqslant)$ be a finite poset. Define the numbers $a_1,a_2,\ldots$ (respectively, $c_1,c_2,\ldots$) so that $a_1+\ldots+a_k$ (respectively, $c_1+\ldots+c_k$) is the maximal number of elements of $\mathcal{P}$ which may be…
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…
Inspired by the Z2Z4-additive codes, linear codes over Z2^r x(Z2+uZ2)^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z2^r x(Z2+uZ2)^s have some advantages…
A partition of a finite poset into chains places a natural upper bound on the size of a union of k antichains. A chain partition is k-saturated if this bound is achieved. Greene and Kleitman proved that, for each k, every finite poset has a…
We show that the separative quotient of the poset (P(L),\subset) of isomorphic suborders of a countable scattered linear order L is \sigma-closed and atomless. So, under the CH, all these posets are forcing-equivalent (to P(\omega)/Fin).
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we determine the explicit complete weight enumerators of two classes of linear codes over $\mathbb{F}_p$ and they…
We establish global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation, under the assumption that the initial data satisfies a partial symmetry condition. These results generalize and…
In this paper, we study the third weight of generalized Reed-Muller codes. We prove under some restrictive condition that the third weight of generalized Reed-Muller codes depends on the third weight of generalized Reed-Muller codes of…
The index coding problem has been generalized recently to accommodate receivers which demand functions of messages and which possess functions of messages. The connections between index coding and matroid theory have been well studied in…
The MacWilliams extension theorem is investigated for various weight functions over finite Frobenius rings. The problem is reformulated in terms of a local-global property for subgroups of the general linear group. Among other things, it is…
We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors…
In this paper, we introduce the concept of the complete cycle index and discuss a relation with the complete weight enumerator in coding theory. This work was motivated by Cameron's lecture note "Polynomial aspects of codes, matroids and…