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51.
We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg
then the state complexity of
is equal to the Wolf bound. For deg
, we use Clifford's theorem to give a simple lower bound on the state complexity of
. We then derive two further lower bounds on the state space dimensions of
in terms of the gonality sequence of
. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of
and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes. 相似文献
52.
By a T
*(2, k, v)-code we mean a perfect4-deletion-correcting code of length 6 over an alphabet of size v, which is capable of correcting anycombination of up to 4 deletions and/or insertions of letters that occur in transmission of codewords. Thethird author (DCC Vol. 23, No. 1) presented a combinatorial construction for such codes and prove thata T
*(2, 6, v)-code exists for all positive integers v 3 (mod 5), with 12 possible exceptions of v. In this paper, the notion of a directedgroup divisible quasidesign is introduced and used to show that a T
*(2, 6,v)-code exists for all positive integers v 3 (mod 5), except possiblyfor v {173, 178, 203, 208}. The 12 missing cases for T
*(2,6, v)-codes with v 3 (mod 5) are also provided, thereby the existenceproblem for T
*(2, 6, v)-codes is almost complete. 相似文献
53.
The structure of linear codes of constant weight 总被引:1,自引:0,他引:1
Jay A. Wood 《Transactions of the American Mathematical Society》2002,354(3):1007-1026
In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.
54.
H. W. Schffer P. H. Mokler R. W. Dunford C. Kozhuharov A. Krmer A. E. Livingston T. Ludziejewski H. -T. Prinz P. Rymuza L. Sarkadi Z. Stachura Th. Sthlker P. Swiat A. Warczak 《Physics letters. A》1999,260(6):331-494
The photon energy differential shape of the second order matrix element for the two-photon (2E1) decay of the 1s2s1S0 level in He-like gold has been measured. The results are in agreement with a recent fully relativistic calculation. The corresponding 2E1 matrix element deviates from those in lighter He-like systems due to the strong central field in a heavy two-electron ion. 相似文献
55.
Tatsuya Maruta 《Geometriae Dedicata》1999,74(3):305-311
Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q –
q - \sqrt q + 2$$
" align="middle" border="0">
and for
when
, which is a generalization of [18, Them. 2.4]. 相似文献
56.
We show that the covering radius R of an [n,k,d] code over Fq is bounded above by R n-n
q(k, d/q). We strengthen this bound when R d and find conditions under which equality holds.As applications of this and other bounds, we show that all binary linear codes of lengths up to 15, or codimension up to 9, are normal. We also establish the normality of most codes of length 16 and many of codimension 10. These results have applications in the construction of codes that attain t[n,k,/it>], the smallest covering radius of any binary linear [n,k].We also prove some new results on the amalgamated direct sum (ADS) construction of Graham and Sloane. We find new conditions assuring normality of the ADS; covering radius 1 less than previously guaranteed for ADS of codes with even norms; good covering codes as ADS without the hypothesis of normality, from concepts p- stable and s- stable; codes with best known covering radii as ADS of two, often cyclic, codes (thus retaining structure so as to be suitable for practical applications). 相似文献
57.
An ordered list of binary words of length n is called a distance-preserving m, n-code, if the list distance between two words is equal to their Hamming distance, for distances up to m. A technique for constructing cyclic m, n-codes is presented, based on the standard Gray code and on some simple tools from linear algebra. 相似文献
58.
David Masson 《Designs, Codes and Cryptography》2003,28(3):283-302
We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules; we define some zonal functions for the symmetric group and we give a closed formula for them, indexed on ordered pair of semi-standard generalized tableaux: Hahn polynomials are a particular case. We derive an algorithm to test if a set is a design. We use it to search designs in some ternary self-dual codes. 相似文献
59.
superconformal algebra is
algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of
algebra are discussed. A new approach to construction of
algebras from rational conformal field theories is proposed. 相似文献
60.
Manju Pruthi 《Proceedings Mathematical Sciences》2001,111(4):371-379
In this paper explicit expressions ofm + 1 idempotents in the ring
are given. Cyclic codes of length 2
m
over the finite fieldF
q, of odd characteristic, are defined in terms of their generator polynomials. The exact minimum distance and the dimension
of the codes are obtained. 相似文献